A grey dynamic model for the evaluation of regional sustainable development and its empirical st

文章编号:1001-8360(2001)05-0107-07基于灰色和模糊集理论的铁路方案多目标综合评价方法及模型研究吴小萍,　詹振炎(中南大学土木建筑学院,湖南长沙　410075)摘　要:分析并指出了铁路可行性研究中经济评价的局限性,提出在着手经济评价的同时,应辅之以多目标综合评价以克服经济评价局限性的思想。

根据铁路方案综合评价各类指标对评价方法的实用性的分析结果,将多种方法组合起来,在此基础上提出了一种新的方法——基于灰色和模糊集理论的铁路方案多目标综合评价方法,并建立其决策模型,编制了该模型的应用软件。

最后,以某快速客运通道方案评价为实例进行验证,结果表明本文建立的模型可以辅助经济评价法获得较为全面的综合评价结果,从而克服经济评价的局限性,为铁路方案综合评价和投资组合决策(pr o tfo lio decisio n ma king)提供了一种新的、有效的方法。

关键词:经济评价;方案决策;多目标决策;综合评价中图分类号:U212 文献标识码:AResearch on multiple-objective decision-making method and model for evaluating railway schemes based on Grey and Fuzzy Sets TheoryW U Xiao-ping,　ZHAN Zhen-yan(Sch ool of Civil and Architecture Eng.,Central Sou th Univ ersity,Changsh a410075,China)Abstract:In this thesis,the limitatio ns of the economic ev alua tion in th e railway feasibility study are analyzed and proposed.B ased o n the analysis of the limitatio ns of the eco nomic ev alua tion,a new m ethod——the multi-ple-objective decisio n-making m ethod fo r evaluating railway schem es based o n the Grey and Fuzzy Sets Theory is put fo rw ard,w hich mea ns com bining v arious metho ds into o ne,and a co rrespo nding model is set up,accord-ing to the analy tical results from the applicatio n of v arious indexes to evaluatio n m ethods of railway schemes and by applying the principle o f multiple-objectiv e decisio n-making and rev olv ing around the solutio n o f such problem.Also its application softw are is intro duced.Finally,taking the synthetic ev alua tion of line schemes applied to o ne ex press railway passag e for ex ample,the results from such ex perim ent can prov e that the deci-sio n making model put fo rwa rd in this thesis can be a pplied to help eco nomic ev aluatio n to g et a rather compre-hensiv e assessment results so as to ov ercome the limitatio ns of the economic assessment,a nd it is a new and ef-fectiv e method fo r the railway synthetic ev aluatio n and protfo lio decision ma king.Keywords:eco nomic evaluatio n;schem es decision;multiple-objectiv e decisio n making;synthetic evaluatio n 铁路方案比选牵涉到投资决策问题,它是通过可行性研究解决的。

Model-Based Inversion of Dynamic Range CompressionStanislaw Gorlow,Student Member,IEEE,and Joshua D.Reiss,Member,IEEEAbstract—In this work it is shown how a dynamic nonlinear time-variant operator,such as a dynamic range compressor,can be inverted using an explicit signal model.By knowing the model parameters that were used for compression one is able to recover the original uncompressed signal from a“broadcast”signal with high numerical accuracy and very low computational complexity.A compressor-decompressor scheme is worked out and described in detail.The approach is evaluated on real-world audio material with great success.Index Terms—Dynamic range compression,inversion, model-based,reverse audio engineering.I.I NTRODUCTIONS OUND or audio engineering is an established discipline employed in many areas that are part of our everyday life without us taking notice of it.But not many know how the audio was produced.If we take sound recording and reproduction or broadcasting as an example,we may imagine that a prerecorded signal from an acoustic source is altered by an audio engineer in such a way that it corresponds to certain criteria when played back.The number of these criteria may be large and usually depends on the context.In general,the said alteration of the input signal is a sequence of numerous forward transformations, the reversibility of which is of little or no interest.But what if one wished to do exactly this,that is to reverse the transfor-mation chain,and what is more,in a systematic and repeatable manner?The research objective of reverse audio engineering is twofold:to identify the transformation parameters given the input and the output signals,as in[1],and to regain the input signal that goes with the output signal given the transformation parameters.In both cases,an explicit signal model is manda-tory.The latter case might seem trivial,but only if the applied transformation is linear and orthogonal and as such perfectly invertible.Yet the forward transform is often neither linear nor invertible.This is the case for dynamic range compressionManuscript received December05,2012;revised February28,2013; accepted February28,2013.Date of publication March15,2013;date of current version March29,2013.This work was supported in part by the “Agence Nationale de la Recherche”within the scope of the DReaM project (ANR-09-CORD-006)as well as the laboratory with which thefirst author is affiliated as part of the“mobilitéjuniors”program.The associate editor coordinating the review of this manuscript and approving it for publication was Prof.Woon-Seng Gan.S.Gorlow is with the Computer Science Research Laboratory of Bordeaux (LaBRI),CNRS,Bordeaux1University,33405Talence Cedex,France(e-mail: stanislaw.gorlow@labri.fr).J.D.Reiss is with the Centre for Digital Music(C4DM),Queen Mary,Uni-versity of London,London E14NS,U.K.(e-mail:josh.reiss@). Digital Object Identifier10.1109/TASL.2013.2253099(DRC),which is commonly described by a dynamic nonlinear time-variant system.The classical linear time-invariant(LTI) system theory does not apply here,so a tailored solution to the problem at hand must be found instead.At this point,we also like to highlight the fact that neither V olterra nor Wiener model approaches[2]–[4]offer a solution,and neither do describing functions[5],[6].These are useful tools when identifying a time-invariant or a slowly varying nonlinear system or ana-lyzing the limit cycle behavior of a feedback system with a static nonlinearity.A method to invert dynamics compression is described in[7], but it requires an instantaneous gain value to be transmitted for each sample of the compressed signal.To provide a means to control the data rate,the gain signal is subsampled and also en-tropy coded.This approach is highly inefficient as it does not rely on a gain model and is extremely generic.On the other hand,transmitting the uncompressed signal in conjunction with a few typical compression parameters like threshold,ratio,attack,and release would require a much smaller capacity and yield the best possible signal quality with regard to any thinkable measure.A more realistic scenario is when the uncompressed signal is not available on the consumer side.This is usually the case for studio music recordings and broadcast material where the listener is offered a signal that is meant to sound“good”to everyone.However,the loudness war [8]has resulted in over-compressed audio material.Over-com-pression makes a song lose its artistic features like excitingness or liveliness and desensitizes the ear thanks to a louder volume. There is a need to restore the original signal’s dynamic range and to experience audio free of compression.In addition to the normalization of the program’s loudness level,the Dolby solution[9],[10]also includes dynamic range expansion.The expansion parameters that help reproduce the original program’s dynamic range are tuned on the broadcaster side and transmitted as metadata together with the broadcast signal.This is a very convenient solution for broadcasters,not least because the metadata is quite compact.Dynamic range ex-pansion is yet another forward transformation rather than a true inversion.Evidently,none of the previous approaches satisfy the re-verse engineering objective of this work.The goal of the present work,hence,is to invert dynamic range compression,which is a vital element not only in broadcasting but also in mastering. The paper is organized as follows.Section II provides a brief introduction to dynamic range compression and presents the compressor model upon which our considerations are based. The data model,the formulation of the problem,and the pur-sued approach are described next in Section III.The inversion1558-7916/$31.00©2013IEEEFig.1.Basic broadband compressor model(feed forward).is discussed in detail in Section IV.Section V illustrates how an integral step of the inversion procedure,namely the search for the zero-crossing of a non-linear function,can be solved in an iterative manner by means of linearization.Some other com-pressor features are discussed in Section VI.The complete al-gorithm is given in the form of pseudocode in Section VII and its performance is evaluated for different compressor settings in Section VIII.Conclusions are drawn in Section IX,where some directions for future work are mentioned.II.D YNAMIC R ANGE C OMPRESSIONDynamic range compression or simply“compression”is a sound processing technique that attenuates loud sounds and/or amplifies quiet sounds,which in consequence leads to a reduc-tion of an audio signal’s dynamic range.The latter is defined as the difference between the loudest and quietest sound mea-sured in decibel.In the following,we will use the word“com-pression”having“downward”compression in mind,though the discussed approach is likewise applicable to“upward”compres-sion.Downward compressing means attenuating sounds above a certain threshold while leaving sounds below the threshold unchanged.A sound engineer might use a compressor to reduce the dynamic range of source material for purposes of aesthetics, intelligibility,recording or broadcast limitations.Fig.1illustrates the basic compressor model from([11],ch.2)amended by a switchable RMS/peak detector in the side chain making it compatible with the compressor/limiter model from ([12],p.106).We will hereafter restrict our considerations to this basic model,as the purpose of the present work is to demon-strate a general approach rather than a solution to a specific problem.First,the input signal is split and a copy is sent to the side chain.The detector then calculates the magnitude or level of the sidechain signal using the root mean square(RMS)or peak as a measure for how loud a sound is([12],p.107). The detector’s temporal behavior is controlled by the attack and release parameters.The sound level is compared with the threshold level and,for the case it exceeds the threshold,a scale factor is calculated which corresponds to the ratio of input level to output level.The knee parameter determines how quick the compression ratio is reached.At the end of the side chain,the scale factor is fed to a smoothingfilter that yields the gain.The response of thefilter is controlled by another set of attack and re-lease parameters.Finally,the gain control applies the smoothed gain to the input signal and adds afixed amount of makeup gain to bring the output signal to a desired level.Such a broad-band compressor operates on the input signal’s full bandwidth, treating all frequencies from zero through the highest frequency equally.A detailed overview of all sidechain controls of a basic gain computer is given in([11],ch.3),e.g.,III.D ATA M ODEL,P ROBLEM F ORMULATION,ANDP ROPOSED S OLUTIONA.Data Model and Problem FormulationThe employed data model is based on the compressor from Fig.1.The following simplifications are additionally made:the knee parameter(“hard”knee)and the makeup gain(fixed at 0dB)are ignored.The compressor is defined as a single-input single-output(SISO)system,that is both the input and the output are single-channel signals.What follows is a description of each block by means of a dedicated function.The RMS/peak detector as well as the gain computer build upon afirst-order(one-pole)lowpassfilter.The sound level or envelope of the input signal is obtained by(1)where represents an RMS detector,and a peak detector.The non-zero smoothing factor,may take on different values,or,depending on whether the detector is in the attack or release phase.The condition for the level detector to enter the attack phase and to choose over is(2)A formula that converts a time constant into a smoothing factor is given in([12],p.109),so e.g.,where is the sampling frequency.The static nonlinearity in the gain computer is usually modeled in the logarithmic domain as a continuous piecewise linear function:(3) where is the slope,,and is the threshold in decibel.The slope is further derived from the de-sired compression ratio according to(4)Equation(3)is equivalently expressed in the linear domain as(5) where,and is the linear scale factor beforefiltering.The smoothed gain is then calculated as the exponentially-weighted moving average,(6) where the decision for the gain computer to choose the attack smoothing factor instead of is subject to(7) The output signal isfinally obtained by multiplying the above gain with the input signal:(8) Due to the fact that the gain is strictly positive,,it follows that(9) where sgn is the signum or sign function.In consequence,it is convenient to factorize the input signal as a product of the sign and the modulus according to(10)The problem at hand is formulated in the following manner: Given the compressed signal and the model parameters recover the modulus of the original signal from based on.For a more intuitive use,the smoothing factors and may be replaced by the time constants and.The meaning of each parameter is listed below.The threshold in dBThe compression ratio dB:dBThe detector type(RMS or peak)The attack time of the envelopefilter in msThe release time of the envelopefilter in msThe attack time of the gainfilter in msThe release time of the gainfilter in msB.Proposed SolutionThe output of the side chain,that is the gain of,given ,and,may be written as(11) In(11),denotes a nonlinear dynamic operator that maps the modulus of the input signal onto a sequence of instanta-neous gain values according to the compressor model rep-resented ing(11),(8)can be solved for yieldingsubject to invertibility of.In order to solve the above equa-tion one requires the knowledge of,which is unavailable. However,since is a function of,we can express as a function of one independent variable,and in that manner we obtain an equation with a single unknown:(12) where represents the entire compressor.If is invertible, i.e.,bijective for all can be obtained from by(13) And yet,since is unknown,the condition for applying decompression must be predicted from,and ,and therefore needs the condition for toggling between the attack and release phases.Depending on the quality of the prediction,the recovered modulus may differ somewhat at transition points from the original modulus,so that in the end(14)In the next section it is shown how such an inverse compressor or decompressor is derived.IV.I NVERSION OF D YNAMIC R ANGE C OMPRESSIONA.Characteristic FunctionFor simplicity,we choose the instantaneous envelope value instead of as the independent variable in(12).The relation between the two items is given by(1).From(6)and(8), when(15)(16) From(1),(17) or equivalently(note that by definition)(18) Moreover,(18)has a unique solution if and also are in-vertible.Moving the expression on the left-hand side over to the right-hand side,we may define(19) which shall be termed the characteristic function.The root or zero-crossing of hence represents the sought-after enve-lope value.Once is found(see Section V),the current values of,and are updated as per(20) and the decompressed sample is then calculated as(21)B.Attack-Release Phase Toggle1)Envelope Smoothing:In case a peak detector is in use, takes on two different values.The condition for the attack phase is then given by(2)and is equivalent to(22) Assuming that the past value of is known at time,what is needed to be done is to express the unknown in terms of such that the above equation still holds true.If is rather small,,or equivalently if is sufficiently large,ms at44.1-kHz sampling,the term in(15)is negligible,so it approximates(15)as(23) Solving(23)for and plugging the result into(22),we obtain(24) If(24)holds true,the detector is assumed to be in the attack phase.2)Gain Smoothing:Just like the peak detector,the gain smoothingfilter may be in either the attack or release phase. The necessary condition for the attack phase in(7)may also be formulated as(25) But since the current envelope value is unknown,we need to substitute in the above inequality by something that is known.With this in mind,(15)is rewritten as(26) Provided that,and due to the fact that ,the expression in square brackets in(26)is smaller than one,and thus during attack(27) Substituting by using(20), and solving(27)for results in(28) If in(25)is substituted by the expression on the right-hand side of(28),(25)still holds true,so the following sufficient condition is used to predict the attack phase of the gainfilter:(29) Note that the values of all variables are known whenever(29)is evaluated.C.Envelope PredictorAn instantaneous estimate of the envelope value is re-quired not only to predict when compression is active,formally according to(5),but also to initialize the iterative search algorithm in Section V.Resorting once more to(15)itcan be noted that in the opposite case where, and so(30) The sound level of the input signal at time is therefore(31) which must be greater than the threshold for compression to set in,whereas and are selected based on(24)and(29), respectively.D.Error AnalysisConsider being estimated from according to(32) The normalized error is then(33)(34) As during attack andduring release,respectively.The instantaneous gain can also be expressed as(35) where is the runtime in ing(35)in(34),the mag-nitude of the error is given by(36)(37) For,(36)becomes(38) whereas for,(37)converges to infinity:(39) So,the error is smaller for large or short.The smallest possible error is for,which then again depends on the current and the previous value of.The error accumulatesifFig.2.Graphical illustration for the iterative search for the zero-crossing.with.The difference between consecutive-values is signal dependent.The signal envelopefluctuates less and is thus smoother for smaller or longer.is also more stable when the compression ratio is low.Foris perfectly constant.The threshold has a negative impact on error propagation.The lower the more the error depends on ,since more samples are compressed with different-values. The RMS detector stabilizes the envelope more than the peak detector,which also reduces the error.Furthermore,since usu-ally,the error due to is smaller during release whereas the error due to is smaller during attack.Finally,the error is expected to be larger at transition points between quiet to loud signal passages.The above error may cause a decision in favor of a wrong smoothing factor in(24),like instead of e.g.,The decision error from(24)then propagates to(29).Given that ,the error due to(32)is accentuated by(24)with the consequence that(29)is less reliable than(24).The total error in(29)thus scales with.In regard to(31),re-liability of the envelope’s estimate is subject to validity of(24) and(29).A better estimate is obtained when the sound level de-tector and the gainfilter are both in either the attack or release phase.Here too,the estimation error increases withand also with.V.N UMERICAL S OLUTION OF THE C HARACTERISTIC F UNCTION An approximate solution to the characteristic function can be found,e.g.,by means of linearization.The estimate from(31) may moreover serve as a starting point for an iterative search of an optimum:The criterion for optimality is further chosen as the deviation of the characteristic function from zero,initialized to(40) Thereupon,(19)may be approximated at a given point using the equation of a straight line,,where is the slope and is the-intercept.The zero-crossing is characterized by the equation(41)as shown in Fig.2.The new estimate of the optimal is found as(42) If is less optimal than,the iteration is stopped and is thefinal estimate.The iteration is also stopped if is smaller than some.In the latter case,has the optimal value with respect to the chosen criterion.Otherwise,is set to and is set to after every step and the procedure is repeated until has converged to a more optimal value.The proposed method is a special form of the secant method with a single initial value.VI.G ENERAL R EMARKSA.Stereo LinkingWhen dealing with stereo signals,one might want to apply the same amount of gain reduction to both channels to prevent image shifting.This is achieved through stereo linking.One way is to calculate the required amount of gain reduction for each channel independently and then apply the larger amount to both channels.The question which arises in this context is which of the two channels was the gain derived from.To give an answer resolving the dilemma of ambiguity,one solution would be to signal which of the channels carries the applied gain.One could then decompress the marked sample and use its gain for the other channel.Although very simple to implement, this approach provokes an additional data rate of44.1kbps at44.1-kHz sampling.A rate-efficient alternative that comes witha higher computational cost is realized in the following way. First,one decompresses both the left and the right channel in-dependently and in so doing one obtains two estimates and,where subscript shall denote the left channel and subscript the right channel,respectively.In a second step,one calculates the compressed values of and and selects the channel for which holds true.In afinal step,one updates the remaining variables using the gain of the selected channel.B.LookaheadA compressor with a look-ahead function,i.e.,with a delay in the main signal path as in([12],p.106),uses past input samples as weighted output samples.Now that some future input sam-ples are required to invert the process—which are unavailable, the inversion is rendered impossible.and must thus be in sync for the approach to be applied.C.Clipping and LimitingAnother point worth mentioning is that“hard”clipping and “brick-wall”limiting are special cases of compression with the attack time set to zero and the compression ratio set to. The static nonlinearity in that particular case is a one-to-many mapping,which by definition is noninvertible.VII.T HE A LGORITHMThe complete algorithm is divided into three parts,each of them given as pseudocode below.Algorithm1out-lines the compressor that corresponds to the model from Sections II–III.Algorithm2illustrates the decompressor de-scribed in Section IV,and the iterative search from Section V isfinally summarized in Algorithm3.The parameter repre-sents the sampling frequency in kHz.function C OMPfor doif thenelseend ifif thenelseend ifif thenelseend ifend forreturnend functionVIII.P ERFORMANCE E VALUATIONA.Performance MetricsTo evaluate the inverse approach,the following quantities are measured:the root-mean-square error(RMSE),(43) given in decibel relative to full scale(dBFS),the perceptual sim-ilarity between the original and decompressed signal,and the execution time of the decompressor relative to real time(RT). Furthermore,we present the percentage of compressed samples, the mean number of iterations until convergence per compressed sample,the error rate of the attack-release toggle for the gainsmoothingfilter,andfinally the error rate of the envelope pre-dictor.The perceptual similarity is assessed by PEMO-Q[13], Algorithm2The decompressorfunction D ECOMPfor doif thenelseend ifif thenelseend ifif thenC HARFZEROelseend ifend forreturnend functionAlgorithm3The iterative search for the zero-crossingfunction C HARFZEROrepeatif thenreturnend ifuntilreturnend function [14]with as metric.The simulations are run in MATLAB on an Intel Core i5-520M CPU.putational ResultsFig.3shows the inverse output signal for a synthetic input signal using an RMS detector.The inverse signal is obtained from the compressed signal with an error of dBFS.It is visually indistinguishable from the original signal.Due to the fact that the signal envelope is con-stant most of the time,the error is noticeable only around tran-sition points—which are few.The decompressor’s performance is further evaluated for some commercial compressor presets. The used audio material consists of12items covering speech, sung voice,music,and jingles.All items are normalized to LKFS[15].The-value in the break condition of Algorithm3 is set to.A detailed overview of compressor settings and performancefigures is given in Tables I–II.The presented results suggest that the decompressed signal is perceptually in-distinguishable from the original—the-value isflawless. This was also confirmed by the authors through informal lis-tening tests.As can be seen from Table II,the largest inversion error is associated with setting E and the smallest with setting B.For allfive settings,the error is larger when an RMS detector is in use.This is partly due to the fact that has a stronger curvature in comparison to.By defining the distance in (40)as,it is possible to attain a smaller error for an RMS detector at the cost of a slightly longer runtime.In most cases,the envelope predictor works more reliably as compared to the toggle switch between attack and release.It can also be observed that the choice of time constants seems to have little impact on decompressor’s accuracy.The major parameters that affect the decompressor’s performance are and,while the threshold is evidently the predominant one:the RMSE strongly correlates with the threshold level.Figs.4–5show the inversion error as a function of various time constants.These are in the range of typical attack and re-lease times for a limiter(peak)or compressor(RMS)([12],pp. 109–110).It can be observed that the inversion accuracy de-pends on the release time of the peak detector and not so much on its attack time for both the envelope and the gainfilter,see Figs.4,5(b).For the envelopefilter,all error curves exhibit a local dip around a release time of0.5s.The error increases steeply below that bound but moderately with larger values.In the proximity of5s,the error converges to dBFS.With regard to the gainfilter,the error behaves in a reverse manner. The curves in Fig.5(b)exhibit a local peak around0.5s with a value of180dBFS.It can further be observed in Fig.4(a) that the curve for ms has a dip where is close to1ms,i.e.,where is minimal.This is also true for Fig.4(c)and(d):the lowest error is where the attack and release times are identical.As a general rule,the error that is due to the attack-release switch is smaller for the gainfilter in Fig.5. Looking at Fig.6one can see that the error decreases with threshold and increases with compression ratio.At a ratio of 10:1and beyond,the RMSE scales almost exclusively with the threshold.The lower the threshold,the stronger the error prop-agates between decompressed samples,which leads to a largerFig.3.An illustrative example using an RMS amplitude detector with set to 5ms,a threshold ofdBFS (dashed line in the upper right corner),acom-pression ratio of 4:1,and set to 1.6ms for attack and 17ms for release,respectively.TheRMSE is dBFS.TABLE IS ELECTED C OMPRESSOR S ETTINGSTABLE IIP ERFORMANCE F IGURES O BTAINED FOR V ARIOUS A UDIO M ATERIAL (12I TEMS )RMSE value.The RMS detector further augments the error be-cause it stabilizes the envelope more than the peak de-tector.Clearly,the threshold level has the highest impact on the decompressor’s accuracy.IX.C ONCLUSION AND O UTLOOKThis work examines the problem of finding an inverse to a nonlinear dynamic operator such as a digital compressor.The proposed approach is characterized by the fact that it uses an explicit signal model to solve the problem.To find the “dry”or uncompressed signal with high accuracy,it is suf ficient to know the model parameters.The parameters can e.g.,be sent together with the “wet”or compressed signal in the form of metadata as is the case with Dolby V olume and ReplayGain [16].A new bit-stream format is not mandatory,since many digital audio stan-dards,like WA V or MP3,provide means to tag the audio con-Fig.4.RMSE as a function of typical attack and release times using a peak (upper row)or an RMS amplitude detector (lower row).In the left column,the attack time of the envelope filter is varied while the release time is held constant.The right column shows the reverse case.The time constants of the gain filter are fixed at zero.In all four cases,threshold and ratio are fixed at 32dBFS and 4:1,respectively.Fig.5.RMSE as a function of typical attack and release times using a peak (upper row)or an RMS amplitude detector (lower row).In the left column,the attack time of the gain filter is varied while the release time is held constant.The right column shows the reverse case.The time constants of the envelope filter are fixed at zero.In all four cases,threshold and ratio are fixed at 32dBFS and 4:1,respectively.tent with “ancillary”data.With the help of the metadata,one can then reverse the compression applied after mixing or be-fore broadcast.This allows the end user to have control over the amount of compression,which may be preferred because the sound engineer has no control over the playback environ-ment or the listener’s individual taste.When the compressor parameters are unavailable,they can possibly be estimated from the compressed signal.This mayFig.6.RMSE as a function of threshold relative to the signal’s average loudness level(left column)and compression ratio(right column)using a peak(upper row)or an RMS amplitude detector(lower row).The time constants are:ms,ms,and s.thus be a direction for future work.Another direction would be to apply the approach to more sophisticated models that include a“soft”knee,parallel and multiband compression,or perform gain smoothing in the logarithmic domain,see[11],[12],[17], [18]and references therein.In conclusion,we want to draw the reader’s attention to the fact that the presentedfigures suggest that the decompressor is realtime capable which can pave the way for exciting new applications.One such application could be the restoration of dynamics in over-compressed audio or else the accentuation of transient components,see[19]–[21],by an adaptively tuned decompressor that has no prior knowledge of the compressor parameters.A CKNOWLEDGMENTThis work was carried out in part at the Centre for Digital Music(C4DM),Queen Mary,University of London.R EFERENCES[1]D.Barchiesi and J.Reiss,“Reverse engineering of a mix,”J.AudioEng.Soc.,vol.58,pp.563–576,2010.[2]T.Ogunfunmi,Adaptive Nonlinear System 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UNIT 1 SCIENCE AND SCIENTISTS1.3 Using Language & Assessing Your Progress一、阅读理解1So you want to be a citizen scientist? The National Science Foundation (NSF) has got you covered. NSF supports citizen science across all areas of science, whether your passion is to scan the night sky, or explore your own backyard.Join a flock of birderseBird is an online platform that allows bird-watchers to go online and record their sightings to a database. With more than 100,000 active users, eBird's system is a treasure of information on bird population, distribution and habitat, which users can explore in real time.Count every dropThe Community Collaborative Rain, Hail and Snow Network (CoCoRaHS)is the largest provider of daily precipitation observations in the United States. V olunteers set up rain gauges and record data every time a rain, snow or hail storm passes over. Data is organized and shared on the CoCoRaHS website, and used by scientists, farmers and more.Search for stars with your computerEinstein@Home uses your computer's idle time to search for space signals. The project has already had major successes: V olunteers discovered about 50 stars, using data from Puerto Rico's Arecibo Observatory and Australia's Parkes Observatory. Einstein@Home also searches for gravitational-wave signals using data from NSF's Laser Interferometer Gravitational Wave Observatory.Be part of a supercomputerTo link all those home computers, Einstien@Home uses software called the Berkeley Open Infrastructure for Network Computing, better known as BOINC. The software choreographs(安排，筹划) the technical aspect of volunteer computing and helps you use radio telescope signals to search for alien life.Join the plankton partyWithout plankton, life in the ocean would not exist. These tiny organisms form the base of the food chain, and play an important role in the global carbon cycle. Plankton Portal enlists citizen scientists to identify images of plankton, snapped by the In Situ Icthyoplankton Imaging System (ISIIS), an underwater robot engineered at the University of Miami. ISIIS has taken millions of images in oceans around the world and upload them into a database; classifying the images helps researchers understand plankton diversity, habitat and behavior.1. On the website of eBird, a bird-watcher can ________.A. make contact with other active usersB. explore the world of birds in real timeC. observe all the existing bird speciesD. provide and share birds’ information2. The program “________” is not based on the Internet database.A. Join the plankton partyB. Be part of a supercomputerC. Count every dropD. Search for stars with your computer3. Which of the following is the best title of the passage?A. Become a Citizen ScientistB. Make a Contribution to NSFC. Be part of Space ExplorationD. Follow the Steps to be a Citizen Scientist【答案】1. D2. B3. A【分析】本文介绍了一些普通老百姓可以参与的科研项目。

The Beginning of Model Checking:A Personal PerspectiveE.Allen Emerson1,21.Department of Computer Sciencesputer Engineering Research CenterThe University of Texas at Austin,Austin TX78712,USAAbstract.Model checking provides an automated method for verify-ing concurrent systems.Correctness specifications are given in tempo-ral logic.The method hinges on an efficient andflexible graph-theoreticreachability algorithm.At the time of its introduction in the early1980’s,the prevailing paradigm for verification was a manual one of proof-theoretic reasoning using formal axioms and inference rules oriented to-wards sequential programs.The need to encompass concurrent programs,the desire to avoid the difficulties with manual deductive proofs,and thesmall model theorem for temporal logic motivated the development ofmodel checking.Keywords:model checking,model-theoretic,synthesis,history,origins1IntroductionIt has long been known that computer software programs,computer hardware designs,and computer systems in general exhibit errors.Working programmers may devote more than half of their time on testing and debugging in order to increase reliability.A great deal of research effort has been and is devoted to developing improved testing methods.Testing successfully identifies many significant errors.Yet,serious errors still afflict many computer systems including systems that are safety critical,mission critical,or economically vital.The US National Institute of Standards and Technology has estimated that programming errors cost the US economy$60B annually[Ni02].Given the incomplete coverage of testing,alternative approaches have been sought.The most promising approach depends on the fact that programs and more generally computer systems may be viewed as mathematical objects with behavior that is in principle well-determined.This makes it possible to specify using mathematical logic what constitutes the intended(correct)behavior.Then one can try to give a formal proof or otherwise establish that the program meets This work was supported in part by National Science Foundation grants CCR-009-8141&CCR-020-5483and funding from Fujitsu Labs of America. email:emerson@ URL:/∼emerson/its specification.This line of study has been active for about four decades now. It is often referred to as formal methods.The verification problem is:Given program M and specification h determine whether or not the behavior of M meets the specification h.Formulated in terms of Turing Machines,the verification problem was considered by Turing[Tu36]. Given a Turing Machine M and the specification h that it should eventually halt (say on blank input tape),one has the halting problem which is algorithmically unsolvable.In a later paper[Tu49]Turing argued for the need to give a(manual) proof of termination using ordinals,thereby presaging work by Floyd[Fl67]and others.The model checking problem is an instance of the verification problem.Model checking provides an automated method for verifying concurrent(nominally)finite state systems that uses an efficient andflexible graph search,to determine whether or not the ongoing behavior described by a temporal property holds of the system’s state graph.The method is algorithmic and often efficient because the system isfinite state,despite reasoning about infinite behavior.If the answer is yes then the system meets its specification.If the answer is no then the system violates its specification;in practice,the model checker can usually produce a counterexample for debugging purposes.At this point it should be emphasized that the verification problem and the model checking problem are mathematical problems.The specification is for-mulated in mathematical logic.The verification problem is distinct from the pleasantness problem[Di89]which concerns having a specification capturing a system that is truly needed and wanted.The pleasantness problem is inherently pre-formal.Nonetheless,it has been found that carefully writing a formal specifi-cation(which may be the conjunction of many sub-specifications)is an excellent way to illuminate the murk associated with the pleasantness problem.At the time of its introduction in the early1980’s,the prevailing paradigm for verification was a manual one of proof-theoretic reasoning using formal axioms and inference rules oriented towards sequential programs.The need to encom-pass concurrent programs,and the desire to avoid the difficulties with manual deductive proofs,motivated the development of model checking.In my experience,constructing proofs was sufficiently difficult that it did seem there ought to be an easier alternative.The alternative was suggested by temporal logic.Temporal logic possessed a nice combination of expressiveness and decidability.It could naturally capture a variety of correctness properties, yet was decidable on account of the“Small”Finite Model Theorem which en-sured that any satisfiable formula was true in somefinite model that was small. It should be stressed that the Small Finite Model Theorem concerns the satisfi-ability problem of propositional temporal logic,i.e.,truth in some state graph. This ultimately lead to model checking,i.e.,truth in a given state graph.The origin and development of model checking will be described below.De-spite being hampered by state explosion,over the past25years model checking has had a substantive impact on program verification efforts.Formal verification2has progressed from discussions of how to manually prove programs correct to the routine,algorithmic,model-theoretic verification of many programs.The remainder of the paper is organized as follows.Historical background is discussed in section2largely related to verification in the Floyd-Hoare paradigm; protocol verification is also considered.Section3describes temporal logic.A very general type of temporal logic,the mu-calculus,that defines correctness in terms offixpoint expressions is described in section4.The origin of model checking is described in section5along with some relevant personal influences on me.A discussion of model checking today is given in section6.Some concluding remarks are made in section7.2Background of Model CheckingAt the time of the introduction of model checking in the early1980’s,axiomatic verification was the prevailing verification paradigm.The orientation of this paradigm was manual proofs of correctness for(deterministic)sequential pro-grams,that nominally started with their input and terminated with their out-put.The work of Floyd[Fl67]established basic principles for proving partial correctness,a type of safety property,as well as termination and total correct-ness,forms of liveness properties.Hoare[Ho69]proposed an axiomatic basis for verification of partial correctness using axioms and inference rules in a formal deductive system.An important advantage of Hoare’s approach is that it was compositional so that the proof a program was obtained from the proofs of its constituent subprograms.The Floyd-Hoare framework was a tremendous success intellectually.It en-gendered great interest among researchers.Relevant notions from logic such as soundness and(relative)completeness as well as compositionality were in-vestigated.Proof systems were proposed for new programming languages and constructs.Examples of proofs of correctness were given for small programs.However,this framework turned out to be of limited use in practice.It did not scale up to“industrial strength”programs,despite its merits.Problems start with the approach being one of manual proof construction.These are formal proofs that can involve the manipulations of extremely long logical formulae. This can be inordinately tedious and error-prone work for a human.In practice, it may be wholly infeasible.Even if strict formal reasoning were used throughout, the plethora of technical detail could be overwhelming.By analogy,consider the task of a human adding100,000decimal numbers of1,000digits each.This is rudimentary in principle,but likely impossible in practice for any human to perform reliably.Similarly,the manual verification of100,000or10,000or even 1,000line programs by hand is not feasible.Transcription errors alone would be prohibitive.Furthermore,substantial ingenuity may also be required on the part of the human to devise suitable assertions for loop invariants.One can attempt to partially automate the process of proof construction using an interactive theorem prover.This can relieve much of the clerical burden.3However,human ingenuity is still required for invariants and various lemmas. Theorem provers may also require an expert operator to be used effectively.Moreover,the proof-theoretic framework is one-sided.It focuses on providing a way to(syntactically)prove correct programs that are genuinely(semantically) correct.If one falters or fails in the laborious process of constructing a proof of a program,what then?Perhaps the program is really correct but one has not been clever enough to prove it so.On the other hand,if the program is really incorrect,the proof systems do not cater for proving incorrectness.Since in practice programs contain bugs in the overwhelming majority of the cases,the inability to identify errors is a serious drawback of the proof-theoretic approach.It seemed there ought to be a better way.It would be suggested by temporal logic as discussed below.Remark.We mention that the term verification is sometimes used in a specific sense meaning to establish correctness,while the term refutation(or falsification) is used meaning to detect an error.More generally,verification refers to the two-sided process of determining whether the system is correct or erroneous.Lastly,we should also mention in this section the important and useful area of protocol work protocols are commonlyfinite state.This makes it possible to do simple graph reachability analysis to determine if a bad state is accessible(cf.[vB78],[Su78]).What was lacking here was aflexible and expres-sive means to specify a richer class of properties.3Temporal LogicModal and temporal logics provided key inspiration for model checking.Origi-nally developed by philosophers,modal logic deals with different modalities of truth,distinguishing between P being true in the present circumstances,pos-sibly P holding under some circumstances,and necessarily P holding under all circumstances.When the circumstances are points in time,we have a modal tense logic or temporal logic.Basic temporal modalities include sometimes P and always P.Several writers including Prior[Pr67]and Burstall[Bu74]suggested that temporal logic might be useful in reasoning about computer programs.For in-stance,Prior suggested that it could be used to describe the“workings of a digital computer”.But it was the seminal paper of Pnueli[Pn77]that made the crit-ical suggestion of using temporal logic for reasoning about ongoing concurrent programs which are often characterized as reactive systems.Reactive systems typically exhibit ideally nonterminating behavior so that they do not conform to the Floyd-Hoare paradigm.They are also typically non-deterministic so that their non-repeatable behavior was not amenable to testing. Their semantics can be given as infinite sequences of computation states(paths) or as computation trees.Examples of reactive systems include microprocessors, operating systems,banking networks,communication protocols,on-board avion-ics systems,automotive electronics,and many modern medical devices.4Pnueli used a temporal logic with basic temporal operators F(sometimes) and G(always);augmented with X(next-time)and U(until)this is today known as LTL(Linear Time Logic).Besides the basic temporal operators applied to propositional arguments,LTL permitted formulae to be built up by forming nestings and boolean combinations of subformulae.For example,G¬(C1∧C2) expresses mutual exclusion of critical sections C1and C2;formula G(T1⇒(T1U C1)specifies that if process1is in its trying region it remains there until it eventually enters its critical section.The advantages of such a logic include a high degree of expressiveness permit-ting the ready capture of a wide range of correctness properties of concurrent programs,and a great deal offlexibility.Pnueli focussed on a proof-theoretic approach,giving a proof in a deductive system for temporal logic of a small example program.Pnueli does sketch a decision procedure for truth overfinite state graphs.However,the complexity would be nonelementary,growing faster than anyfixed composition of exponential functions,as it entails a reduction to S1S,the monadic Second order theory of1Successor,(or SOLLO;see be-low).In his second paper[Pn79]on temporal logic the focus is again on the proof-theoretic approach.I would claim that temporal logic has been a crucial factor in the success of model checking.We have one logical framework with a few basic temporal operators permitting the expression of limitless specifications.The connection with natural language is often significant as well.Temporal logic made it possible, by and large,to express the correctness properties that needed to be expressed. Without that ability,there would be no reason to use model checking.Alternative temporal formalisms in some cases may be used as they can be more expressive or succinct than temporal logic.But historically it was temporal logic that was the driving force.These alternative temporal formalisms include:(finite state)automata(on infinite strings)which accept infinite inputs by infinitely often entering a desig-nated set of automaton states[Bu62].An expressively equivalent but less succinct formalism is that ofω-regular expressions;for example,ab cωdenotes strings of the form:one a,0or more b s,and infinitely many copies of c;and a property not expressible in LTL(true P)ωensuring that at every even moment P holds. FOLLO(First Order Language of Linear Order)which allows quantification over individual times,for example,∀i≥0Q(i);and SOLLO(Second Order Language of Linear Order)which also allows quantification over sets of times corresponding to monadic predicates such as∃Q(Q(0)∧∀i≥0(Q(i)⇒Q(i+1)).1These alterna-tives are sometimes used for reasons of familiarity,expressiveness or succinctness. LTL is expressively equivalent to FOLLO,but FOLLO can be nonelementarily more succinct.This succinctness is generally found to offer no significant practi-cal advantage.Moreover,model checking is intractably(nonelementarily)hard for FOLLO.Similarly,SOLLO is expressively equivalent toω−regular expres-sions but nonelementarily more succinct.See[Em90]for further discussion.1Technically,the latter abbreviates∃Q(Q(0)∧∀i,j≥0(i<j∧¬∃k(i<k<j))⇒(Q(i)⇒Q(j)).5Temporal logic comes in two broad styles.A linear time LTL assertion h is interpreted with respect to a single path.When interpreted over a program there is an implicit universal quantifications over all paths of the program.An assertion of a branching time logic is interpreted over computation trees.The universal A (for all futures)and existential E(for some future)path quantifiers are important in this context.We can distinguish between AF P(along all futures,P eventually holds and is thus inevitable))and EF P(along some future,P eventually holds and is thus possible).One widely used branching time logic is CTL(Computation Tree Logic)(cf. [CE81]).Its basic temporal modalities are A(for all futures)or E(for some fu-ture)followed by one of F(sometime),G(always),X(next-time),and U(until); compound formulae are built up from nestings and propositional combinations of CTL subformulae.CTL derives from[EC80].There we defined the precursor branching time logic CTF which has path quantifiers∀fullpath and∃fullpath, and is very similar to CTL.In CTF we could write∀fullpath∃state P as well as ∃fullpath∃state P These would be rendered in CTL as AF P and EF P,respec-tively.The streamlined notation was derived from[BMP81].We also defined a modal mu-calculus FPF,and then showed how to translate CTF into FPF. The heart of the translation was characterizing the temporal modalities such as AF P and EF P asfixpoints.Once we had thefixpoint characterizations of these temporal operators,we were close to having model checking.CTL and LTL are of incomparable expressive power.CTL can assert the existence of behaviors,e.g.,AGEF start asserts that it is always possible to re-initialize a circuit.LTL can assert certain more complex behaviors along a computation,such as GF en⇒F ex relating to fairness.(It turns out this formula is not expressible in CTL,but it is in“FairCTL”[EL87])The branching time logic CTL*[EH86]provides a uniform framework that subsumes both LTL and CTL,but at the higher cost of deciding satisfiability.There has been an ongoing debate as to whether linear time logic or branching time logic is better for program reasoning(cf.[La80],[EH86],[Va01]).Remark.The formal semantics of temporal logic formulae are defined with respect to a(Kripke)structure M=(S,S0,R,L)where S is a set of states,S0 comprises the initial states,R⊆S×S is a total binary relation,and L is a labelling of states with atomic facts(propositions)true there.An LTL formula h such as F P is defined over path x=t0,t1,t2...through M by the rule M,x|= F P iff∃i≥0P∈L(t i).Similarly a CTL formula f such as EGP holds of a state t0,denoted M,t0|=EGP,iffthere exists a path x=t0,t1,t2,...in M such that∀i≥0P∈L(t i).For LTL h,we define M|=h ifffor all paths x starting in S0,M,x|=h.For CTL formula f we define M|=f ifffor each s∈S0,M,s|=f.A structure is also known as a state graph or state transition graph or transition system.See[Em90]for details.64The Mu-calculusThe mu-calculus may be viewed as a particular but very general temporal logic. Some formulations go back to the work of de Bakker and Scott[deBS69];we deal specifically with the(propositional or)modal mu-calculus(cf.[EC80],[Ko83]). The mu-calculus provides operators for defining correctness properties using re-cursive definitions plus leastfixpoint and greatestfixpoint operators.Leastfix-points correspond to well-founded or terminating recursion,and are used to capture liveness or progress properties asserting that something does happen. Greatestfixpoints permit infinite recursion.They can be used to capture safety or invariance properties.The mu-calculus is very expressive and veryflexible.It has been referred to as a“Theory of Everything”.The formulae of the mu-calculus are built up from atomic proposition con-stants P,Q,...,atomic proposition variables Y,Z,...,propositional connectives ∨,∧,¬,and the leastfixpoint operator,µas well as the greatestfixpoint opera-tor,ν.Eachfixpoint formula such asµZ.τ(Z)should be syntactically monotone meaning Z occurs under an even number of negations,and similarly forν.The mu-calculus is interpreted with respect to a structure M=(S,R,L). The power set of S,2S,may be viewed as the complete lattice(2S,S,∅,⊆,∪,∩).Intuitively,each(closed)formula may be identified with the set of states of S where it is true.Thus,false which corresponds to the empty set is the bottom element,true which corresponds to S is the top element,and implication (∀s∈S[P(s)⇒Q(s)])which corresponds to simple set-theoretic containment (P⊆Q)provides the partial ordering on the lattice.An open formulaτ(Z) defines a mapping from2S→2S whose value varies as Z varies.A givenτ: 2S→2S is monotone provided that P⊆Q impliesτ(P)⊆τ(Q).Tarski-Knaster Theorem.(cf.[Ta55],[Kn28])Letτ:2S→2S be a monotone functional.Then(a)µY.τ(Y)=∩{Y:τ(Y)=Y}=∩{Y:τ(Y)⊆Y},(b)νY.τ(Y)=∪{Y:τ(Y)=Y}=∪{Y:τ(Y)⊇Y},(c)µY.τ(Y)=∪iτi(false)where i ranges over all ordinals of cardinality at mostthat of the state space S,so that when S isfinite i ranges over[0:|S|],and (d)νY.τ(Y)=∩iτi(true)where i ranges over all ordinals of cardinality at mostthat of the state space S,so that when S isfinite i ranges over[0:|S|].Consider the CTL property AF P.Note that it is afixed point orfixpoint of the functionalτ(Z)=P∨AXZ.That is,as the value of the input Z varies,the value of the outputτ(Z)varies,and we have AF P=τ(AF P)=P∨AXAF P. It can be shown that AF P is the leastfixpoint ofτ(Z),meaning the set of states associated with AF P is a subset of the set of states associated with Z,for any fixpoint Z=τ(Z).This might be denotedµZ.Z=τ(Z).More succinctly,we normally write justµZ.τ(Z).In this case we have AF P=µZ.P∨AXZ.We can get some intuition for the the mu-calculus by noting the following fixpoint characterizations for CTL properties:7EF P=µZ.P∨EXZAGP=νZ.P∧AXZAF P=µZ.P∨AXZEGP=νZ.P∧EXZA(P U Q)=µZ.Q∨(P∧AXZ)E(P U Q)=µZ.Q∨(P∧EXZ)For all these properties,as we see,thefixpoint characterizations are simple and plausible.It is not too difficult to give rigorous proofs of their correctness (cf.[EC80],[EL86]).We emphasize that the mu-calculus is a rich and powerful formalism;its formulae are really representations of alternatingfinite state au-tomata on infinite trees[EJ91].Since even such basic automata as deterministic finite state automata onfinite strings can form quite complex“cans of worms”, we should not be so surprised that it is possible to write down highly inscrutable mu-calculus formulae for which there is no readily apparent intuition regard-ing their intended meaning.The mu-calculus has also been referred to as the “assembly language of program logics”reflecting both its comprehensiveness and potentially intricate syntax.On the other hand,many mu-calculus char-acterizations of correctness properties are elegant due to its simple underlying mathematical organization.In[EL86]we introduced the idea of model checking for the mu-calculus in-stead of testing satisfiability.We catered for efficient model checking in fragments of the the mu-calculus.This provides a basis for practical(symbolic)model checking algorithms.We gave an algorithm essentially of complexity n d,where d is the alternation depth reflecting the number of significantly nested least and greatestfixpoint operators.We showed that common logics such as CTL,LTL, and CTL*were of low alternation depth d=1or d=2.We also provided succinctfixpoint characterizations for various natural fair scheduling criteria.A symbolic fair cycle detection method,known as the“Emerson-Lei”algorithm, is comprised of a simplefixpoint characterization plus the Tarski-Knaster theo-rem.It is widely used in practice even though it has worst case quadratic cost. Empirically,it usually outperforms alternatives.5The Origin of Model CheckingThere were several influences in my personal background that facilitated the de-velopment of model checking.In1975Zohar Manna gave a talk at the University of Texas onfixpoints and the Tarski-Knaster Theorem.I was familiar with Di-jkstra’s book[Di76]extending the Floyd-Hoare framework with wlp the weakest liberal precondition for partial correctness and wp the weakest precondition for to-tal correctness.It turns out that wlp and wp may be viewed as modal operators, for which Dijkstra implicitly gavefixpoint characterizations,although Dijkstra did not favor this viewpoint.Basu and Yeh[BY75]at Texas gavefixpoint char-acterizations of weakest preconditions for while loops.Ed Clarke[Cl79]gave similarfixpoint characterizations for both wp and wlp for a variety of control structures.8I will now describe how model checking originated at Harvard University.In prior work[EC80]we gavefixpoint characterizations for the main modalities of a logic that was essentially CTL.These would ultimately provide thefirst key ingredient of model checking.Incidentally,[EC80]is a paper that could very well not have appeared.Some-how the courier service delivering the hard-copies of the submission to Amster-dam for the program chair at CWI(Dutch for“Center for Mathematics and Computer Science”)sent the package in bill-the-recipient mode.Fortunately, CWI was gracious and accepted the package.All that remained to undo this small misfortune was to get an overseas bank draft to reimburse them.The next work,entitled“Design and Synthesis of Synchronization Skeletons using Branching Time Logic”,was devoted to program synthesis and model checking.I suggested to Ed Clarke that we present the paper,which would be known as[CE81],at the IBM Logics of Programs workshop,since he had an invitation to participate.Both the idea and the term model checking were introduced by Clarke and Emerson in[CE81].Intuitively,this is a method to establish that a given program meets a given specification where:–The program defines afinite state graph M.–M is searched for elaborate patterns to determine if the specification f holds.–Pattern specification isflexible.–The method is efficient in the sizes of M and,ideally,f.–The method is algorithmic.–The method is practical.The conception of model checking was inspired by program synthesis.I was interested in verification,but struck by the difficulties associated with manual proof-theoretic verification as noted above.It seemed that it might be possible to avoid verification altogether and mechanically synthesize a correct program directly from its CTL specification.The idea was to exploit the small model property possessed by certain decidable temporal logics:any satisfiable formula must have a“small”finite model of size that is a function of the formula size. The synthesis method would be sound:if the input specification was satisfiable, it built afinite global state graph that was a model of the specification,from which individual processes could be extracted The synthesis method should also be complete:If the specification was unsatisfiable,it should say so.Initially,it seemed to me technically problematic to develop a sound and complete synthesis method for CTL.However,it could always be ensured that an alleged synthesis method was at least sound.This was clear because given anyfinite model M and CTL specification f one can algorithmically check that M is a genuine model of f by evaluating(verifying)the basic temporal modal-ities over M based on the Tarski-Knaster theorem.This was the second key ingredient of model posite temporal formulae comprised of nested subformulae and boolean combinations of subformulae could be verified by re-cursive descent.Thus,fixpoint characterizations,the Tarski-Knaster theorem, and recursion yielded model checking.9Thus,we obtained the model checking framework.A model checker could be quite useful in practice,given the prevalence offinite state concurrent systems. The temporal logic CTL had theflexibility and expressiveness to capture many important correctness properties.In addition the CTL model checking algorithm was of reasonable efficiency,polynomial in the structure and specification sizes. Incidentally,in later years we sometimes referred to temporal logic model check-ing.The crucial roles of abstraction,synchronization skeletons,andfinite state spaces were discussed in[CE81]:The synchronization skeleton is an abstraction where detail irrelevant to synchronization is suppressed.Most solutions to synchronization prob-lems are in fact given as synchronization skeletons.Because synchronization skeletons are in generalfinite state...proposi-tional temporal logic can be used to specify their properties.Thefinite model property ensures that any program whose synchroniza-tion properties can be expressed in propositional temporal logic can be realized by afinite state machine.Conclusions of[CE81]included the following prognostications,which seem to have been on target:[Program Synthesis]may in the long run be quite practical.Much addi-tional research will be needed,however,to make it feasible in practice....We believe that practical[model checking]tools could be developed in the near future.To sum up,[CE81]made several contributions.It introduced model check-ing,giving an algorithm of quadratic complexity O(|f||M|2).It introduced the logic CTL.It gave an algorithmic method for concurrent program synthesis(that was both sound and complete).It argued that most concurrent systems can be abstracted tofinite state synchronization skeletons.It described a method for efficiently model checking basic fairness using strongly connected components. An NP-hardness result was established for checking certain assertions in a richer logic than CTL.A prototype(and non-robust)model checking tool BMoC was developed,primarily by a Harvard undergraduate,to permit verification of syn-chronization protocols.A later paper[CES86]improved the complexity of CTL model checking to linear O(|f||M|).It showed how to efficiently model check relative to uncondi-tional and weak fairness.The EMC model checking tool was described,and a version of the alternating bit protocol verified.A general framework for efficiently model checking fairness properties was given in[EL87],along with a reduction showing that CTL*model checking could be done as efficiently as LTL model checking.Independently,a similar method was developed in France by Sifakis and his student[QS82].Programs were interpreted over transition systems.A branching10。

U1acquisition thrust concentration distinctive specifically distinguish evidently diminishadjust function1. The risk from viruses certainly hasn't diminished ; on the contrary, it has mushroomed and people can easily get infected with virus.2. I like wild sunflower not because it has a(n) distinctive North American flavor but because its image is closely connected with our continent's early history.3. One of the main characteristics that distinguish the male bird from female bird is that the former has beautiful feathers.4. He went to apply for hundreds of jobs with a master's degree in computer science but ended up with nothing. Evidently, it's because he was disabled.5. Some books are specially designed to tell us information about the social, cultural or professional life of the country.6. I was embarrassed as an American for having thrust such an awful concept upon the French, saying that the French hated the idea of the theme park, Euro Disney.7. In places where it does not rain very often, the function of canals is to drain water from rivers or lakes and carry it to fields.8. There is also evidence of slower acquisition of language and a higher frequency of learning difficulties for these physically disabled students.9. If you must sit facing the desk, shift your chair slightly as you sit down or adjust your body in the chair slightly so that you can be right in front of your interviewer.10. Clever readers focus their attention, keeping their concentration on the material they know best and answering questions quickly because they are confident.assembly moist earnest destinationmoisture proclaim asset questrally exclaim1. Last Saturday, about 5,000 people held a protest march and rally against social discrimination against all people with AIDS.2. When appearing in court, my friend Debra exclaimed in anger to a judge to defend her actions, "I wasn't hurting anyone!"3. Human beings shall enjoy freedom of speech and belief, which has been proclaimed as the highest aspiration of the common people.4. Henry Ford was one of the first to apply assembly line manufacturing to the mass production of affordable automobiles.5. Unless you have a heated greenhouse, you will have difficulty in keeping the plant indoors for very long because they need a really warm and moist atmosphere.6. In dry weather, you'd better water your vegetables, flowers, and plants in the morning before the earth loses too much moisture .7. When you are faced with a difficult situation, you may rely on some of your assets such as family, friends, skills, education, money, and good health.8. After many years' searching of the world, her quest for her missing brother finally succeeded when she found him in Africa9. She decided long ago that she would study the subject of physics in earnest as soon as she was accepted by the school.10. He regretted that he hadn't followed his friend's suggestion. If he had taken the short-cut across the river, he would have arrived at the destination much earlier.A. fluentB. acquisitionC. diverseD. reverseE. competentF. competitiveG. skim H. beneficial I. enhanceJ. engage K. comprehension L. confusionM. proficiency N. exposure O. efficiencyTesting has replaced teaching in most public schools. Instead of teaching reading or writing skills which are beneficial to students, now teachers are somehow encouraged to reverse the learning process. For instance, they ask students to read the questions at the end of a reading text first, and then teach them to skim the text for the answers with various test-taking skills. We wonder whether the test-taking skills really help improve their language proficiency.The ability to read or write should enhance the ability to do reasonably well on comprehension of reading texts or fluent writing. However, neither reading nor writing develops simply through learning test-taking skills. Teachers must be careful when they teach students how to read and write to avoid any false language acquisition . Too many discussions on test-taking skills will only end up with more confusion in learning because students have become more interested in test-taking skills rather than concentrating on the nature and quality of what should be taught.As a result, students may be competent in taking tests while they have little or no exposure to serious reading or thinking. They are unable to understand or talk about what they read, which is definitely disastrous to their academic preparation.U2persist boost invest orientevaluate accumulate accelerate calculatespeculate undertake1. The United Nations official said to undertake a new peace move in the Middle East when there is a chance to reach an agreement.2. We might speculate further from the story and say that these people probably lived very close to the well because of the importance of water to life.3. As they are not sure about the situation in the flood-stricken area, they will first send trained nurses there to evaluate the needs of each patient.4. If the extremely hostile relationships tend to persist , the conflicts between the two parties make it difficult to recognize that they share common needs and goals.5. As more students are inclined to choose business as their major, the college has to offer more courses that are business- oriented .6. If workers believe inflation is likely to accelerate , they will demand higher wages to compensate for expected increases in prices.7. If you have a good planning to set aside 500 dollars per month, it would take two years to accumulated the minimum sum needed for your child.8. If the population continues to rise at the present rate, scientists have calculated that the world's population will double by the end of the century.9. The cost of repairing damaged public facilities is so high that some local governments are unwilling to invest in the rebuilding projects.10. According to recent research reports, learning a new dance step may boost the brain in the same way that learning a language does.liable liberal unconscious objective promising realistic sufficient dominantcynical destructive1. Both parents and teachers are very concerned about the destructive effects that violent films may have on children.2. If you keep interrupting me, it is unlikely that I will have sufficient time to give you the complete picture which you are so anxious to get!3. The new method is both reliable and objective ; furthermore, it has benefited greatly from the development of computer technology.4. Of all the media, the Internet is clearly dominant , with television a close second, at least as a source of news and other information.5. Body movements are often unconscious forms of expressions, and they can convey certain information to the audience.6. The school principal has some liberal views about what his students should wear and how much freedom should allow them.7. Word meanings are especially liable to change because people learn them by hearing them in context rather than by looking up the standard definition.8. The company seems promising because the electronic and printing unit alone has annual sales of about $80 million.9. During the time of economic depression, many people may seem to be cynical about what the government might do, and they just cannot believe the wealthy officials. 10. The bottom line is that I have tried to be true to myself at all times and in all situations, and I simply don't think it is realistic to expect anything else.enroll bother install investrecruit reform revise shrink acknowledge confirm1. Steve Jobs has been acknowledged as a genius in business; his greatest skills are his insight, creative mind, and his management ability.2. To keep the companies going, firms need to recruit candidates frequently to replace those who choose not to continue their contracts.3. I believe I have to revise my ideas about my boss —he's stubborn sometimes but very clever and creative in many cases.4. In order to improve their job skills —to get new jobs or to advance in the ones they already have, many enroll in some forms of continuing education courses.5. In business settings, email is best used to convey some key information, to confirm appointments, to document decisions, or to contact a decision maker directly.6. Wetland losses have caused populations of some bird species —starved for water, food, and nesting sites —to shrink by 60 to 80 percent.7. Better technology means you can install more sensitive alarm systems in your home and carry less cash on the street.8. The name Joe particularly bothers me as some think it makes me more qualified to be a baseball player rather than an art critic.9. We can surely reform our public health care system, but it still gives us, for all its flaws, the best health care in the world.10. The manual labor in the countryside for 10 years had invested him with a strong will and perseverance to overcome difficulties.A. calculateB. assertsC. distinguishD. literallyE. securedF. broadenedG. performs H. insight I. accumulateJ. inserts K. just L. extremelyM. bound N. perceive O. sightWhy study the humanities? The 19th-century English philosopher John StuartMill asserts that, instead of places for pure learning, universities ought to be places that literally encourage students to become good human beings.This assertion may sound out-of-date since most college students today are bound to learn knowledge and special skills. According to Mill, human beings are just human beings before they are lawyers or doctors. Mill further explains that a strong liberal arts curriculum will make lawyers or doctors see differently with broadened horizons.But can someone be a successful lawyer of great inner insight without studying the humanities? Yes. Can someone succeed in business or medicine without the liberal arts? Sure. But we ought to distinguish"the goodness of the operation" from the "goodness of the operator". How well someone performs in a specialized field is not necessary to do with how well a person behaves as a good human being.The study of the humanities, therefore, prepares students for their future "philosophic habit of mind" —something extremely different from an Internet and Information Age which values speed and instant satisfaction. On the contrary, studying the humanities enables us to accumulate slow, on-going knowledge to respond to the basic questions of our age, a means of human betterment.U3deceive distract confuse hesitatesnap rouse affirm surrenderwitness acquaint1. More and more unexpected stress and pressure began to get to her, and one morning she just snapped as she could no longer bear them.2. The young and handsome speaker was standing in front of a large crowd of people, attempting to rouse the crowd with a cry for action.3. No matter where we are, we must not let cultural, racial, or social barriers distract us from the job that must be done on our responsibility.4. The government has surrendered itself to the pressure from big business and companies and eventually brought down interest rates.5. The fresh air and bright sunlight deceived me into thinking I might still have some youthful energy left in these old bones of mine.6. The man denied having witnessed the accident because he was afraid of getting himself involved in a long process of investigation.7. The press gave a completely different version of the events, which greatly confused those who tried to understand the truth.8. He continued to affirm that the introduction of divorce would make it more difficult for people to lead "good moral lives".9. Staff members were asked to acquaint themselves with what had been discussed and covered if they were absent from the meeting yesterday.10. The young writer hesitated , reluctant to destroy any part of his own work, for which he had devoted all his time for quite a few years.equivalent static chaotic alertfeasible coarse stable implicitrefined sensible1. It's understandable that at 15,000 feet, no pilot who is already suffering from the effects of lack of oxygen will be able to make sensible decisions.2. English law says that circumstances of a marriage aren't static, and therefore a judge should decide how financial assets will be divided in cases of divorce.3. Contrary to young people, mature adults would prefer to choose some professions that are stable and could bring prestige and economic benefits.4. The new manager of the company complained several times that he could not work effectively under such chaotic conditions.5. She didn't openly attack the plan, but the fact that she was against it was implicit in her silence when others were saying things in support of it.6. Reserved speaking style and refined manners are always considered characteristic of English gentlemen.7. I respected her because she was very polite and, like the rest of her people, never laughed if an outsider said something coarse .8. Now that we have the extra resources from the local government, the long-term project started a year ago seems economically feasible .9. Passengers on the plane were told to stay alert at all times and report any suspicious packages to the crew members immediately.10. Several games based on the "Star Wars" movies require players to choose between the light and dark sides of the Force, equivalent to good and evil.A. mysteriousB. previousC. fluidD. liquidE. indispensableF. stableG. miserable H. labeled I. shiftJ. implicit K. exploit L. exploreM. tends N. intends O. frameI don't want any sort of traditional stability in my life right now. The thought of marriage, staying in one place and doing one thing, will make me feel miserable because there are too many things on my to-do list. Don't take me wrong that I won't shift to marriage, but certainly not yet.The previous four common life phases, childhood, adolescence, adulthood and old age, are now added with two more, labeled"odyssey" and "active retirement". Of the new ones, the less understood is odyssey that frequently occurs between adolescence and adulthood.For our parents' generation, adulthood tends to be defined by achieving certain things. We all know them –owning a house, having a stable career, getting married and ultimately having children.We use "finding ourselves" to frame the concept of the odyssey years, but it's more important for us to understand the implicit meaning: the pursuit of knowledge and making use of the accessibility of information and experiences around us.In a time when everything is fluid, it seems that the old recipes and time frames for accomplishing things don't apply. We don't have the same expectations as we once had.We explore to find our own meanings to things and give voices to our hearts. It seems it becomes more important to find out why we are here before we choose to settle.A. diminishedB. demonstratedC. alertD. radicalE. surrenderF. surviveG. affirms H. afford I. affectJ. effect K. soaked L. soapedM. sensitive N. sensible O. somehowTeenagers are different from people of other age groups. The differences canbe demonstrated from how they behave. In fact, the brains of teenagers are very different from those of children or adults.Once people believed it was sensible that the human brain was fully developed by the age of three. According to this theory, teenager behaviors like risk-taking, a lack of sensitivity to how their actions affect both themselves and others, increased aggressive deeds, diminished concentration and a negative attitude were thought to be due to bad parenting or changes in body chemistry.However, new technology has allowed researchers to examine the healthy brain at work. What they have discovered is something radical: Not only does the brain continue to grow beyond the age of three, but the research also affirms that the brain of a teenager is larger than that of an adult.As teen brains are soaked with chemicals during adolescence phase, the brain grows. However, only the cells that are used the most will survive the competition within the brain. Those that are used less begin to die off until the brain reaches what will be its adult size.The way that teens spend their time somehow influences which connections remain and which disappear. On the basis of this knowledge, experts advise parents tobe alert on how their teenagers spend their time. What teens do today will affect their brains for the rest of their lives.U4ambitious cautious immune dynamic preliminary indifferent pessimistic superb weird abnormal1. Even though the global economic situation is pessimistic , not everyone is so pessimistic about the future. They believe it will be recovered in a few years.2. The lab director said that the experiment was at its preliminary stage and they would need more time to come to a final result.3. The local people have been so realistic and cautious about any changes that the progress of reform has been very slow.4. The U.S. is definitely a telephone country. This is partly due to the fact that the telephone service is superb there, whereas the postal service is less efficient.5. Although we did a lot better than most or even than our own expectations, we are not entirely immune to that criticism from those who are trying to find fault with us.6. While the occurrences in Bermuda Triangle have been reported that the area is filled with weird happenings, he was not apparently disturbed by what he had seen.7. I truly believe I would not be the strong and ambitious person as I am today if I did not have a hearing disability, an innate physical problem.8. Many reports show that earthquake occurrences can be predicted by abnormal animal behavior that can be seen minutes as well as weeks before the events.9. The University of London is located in one of the world's most dynamic cities, which can offer international students an exciting cultural life as well as the very best course choice.10. Before the competition, she assumed that she had a winner on her hands, but her indifference to the rivals led to her ultimate failure.thrill incline weave forgefrown impulse initiative contact consequently exceedingly1. We all buy goods on impulse sometimes, simply because we saw them on the shelf of the shop and they looked tempting.2. My coach checked his watch and frowned , "This is not acceptable for a promising young athlete like you." I lowered my head, pretending to feel shame.3. While the population has increased only 40 percent since 1960, violent crime in America has increased 550 percent, so Americans are exceedingly worried about it.4. Believe me, it's a real thrill to see my own story published in a national newspaper and so favorably reviewed by famous critics.5. Children with parents whose guidance is firm, consistent, and rational are inclined to be straightforward and possess high levels of self-confidence.6. I bought a used car last month, and it often caused trouble. Yesterday, my car broke down again and consequently I was late for my physics class.7. AIDS spreads in three basic ways: first, through sexual intercourse; second, through contact with diseased blood; and third from an HIV mother to her baby.8. Under the poet's wide imaginations, nature and mystery were woven into the poems –along with fear and sophisticated ideas, so it's hard for readers to understand.9. Because of a stupid mistake in our decision-making process, we lost the chance to take the initiative in the business deal; the other side has taken advantage of it now.10. You are the person who is responsible and enthusiastic, making our work possible, so I'll try to forge more reliable links between us.A. dictateB. deserveC. makeD. reserveE. charityF. formulaG. security H. demanding I. daringJ. fallen K. lack L. desirableM. available N. haste O. superiorChoosing a husband or wife is one of the most important decisions in a person's life. In many cultures, young men and women are daring to choose their own marriage partners. In some cultures, however, parents reserve the right to arrange their children's marriages. Such arranged marriages have both advantages and disadvantages.One advantage of having parents arrange a marriage is financial security. Of course, money doesn't automatically bring happiness, but a lack of money certainly causesstress in any relationship. A second advantage of an arranged marriage is that parents may make a better choice than their children. They are not only older but also more superior in life experience. Also, parents have been married; therefore, they know better what qualities are desirable in a spouse.On the other hand, arranged marriages may have some disadvantages. One obvious disadvantage is that parents may choose a wrong person in haste, and the young couple may never be happy together. A second obvious disadvantage is that a young man or woman may already have fallen in love with someone else. If the parents force their children to tie the knot, the result will be a disaster to all concerned.In conclusion, neither an arranged marriage nor a marriage for love is a good formula to be happy. Both kinds of marriages take work, patience, and perhaps a little bit of luck.U5defy contradict disguise derivesubmit remedy manufacture manipulatescout issue1. The global increase in house prices is a boom by design, largely manufactured by the world's central banks, led by the Federal Reserve.2. He was accused of manipulating the price of a stock by illegal means so he could buy it cheaply. Many stock holders were so angry about the scandal.3. I saw a group of people scouting the hills for a nuclear test site though they knew it might possibly cause severe and permanent damage to the environment.4. It is surprising that fewer students were prepared to submit written work on a regular basis or to study over long periods.5. Even though he was issued an explicit warning, he still insisted on having his own way, which eventually led to this disaster.6. Even though love is considered noble and pure, the open nature of the true love contradicts the fact that love is often selfish and ego-centered.7. To regulate school policies on cheating and improper behavior among students, those who defy rules and cheat in exams will be forced to drop out.8. The German soldiers disguised themselves as English troops, but their accents gave them away, so they were finally discovered by the English officers.9. Ever since the peace crisis started in the Middle East, a great deal has been done internationally to remedy the situation in that area.10. He believes that all scientists should derive their theories from the first hand experiments and approved research.hinder prohibit filter shrugstagger retain resume suspendimpose dissolve1. In some countries churches are not allowed to impose their beliefs on people, but they are allowed to practice their faith freely.2. Even though the oil price is increasing all the time, it was given another push up this week when Iraq suspended oil exports for domestic armed conflicts.3. Since the natural processes for filtering water can clean only a certain amount of water by removing the pollution, new technique must be introduced for purified water.4. The Beatles dissolved in 1970, but the Rolling Stones were still performing in the 1990s, being active and famous for more than thirty years.5. Since many car accidents are related with distracted driving, now at least 25 countries restrict or prohibit the use of cell phones and other wireless technology while driving.6. Unless a child's daydreaming is hindering him from progressing in school or from gaining social skills, there is no need to discourage it.7. Even though he was not very popular among his colleagues, he staggered everyone by suddenly announcing that he was leaving the company at the end of the month. 8. People can figure out the meaning of certain gestures or body languages. He shrugged his shoulders as if there was nothing he could do about it.9. The Bosnian peace-talks are resuming in Geneva in a couple of days with the up-to-date proposals at the top of the agenda.10. Paul Allen has made quite an impact on the region and the world. In 2000, he retired from Microsoft, but the company retained him as a permanent advisor to top executives.A. perspectiveB. initiativeC. optionD. portionE. principleF. principalG. explicit H. implicit I. seemJ. assume K. resume L. suspendedM. suspected N. tackle O. fundsI'm often asked how much spending money college students need. While that may seem like a simple question, the answer is different for each student and family. Iwill suggest a way for each student and family to find out for themselves. Obviously, I assume the family is providing some financial support to the student for college. This is both because I think it's the norm AND because I think parents have no option. Remember, I also think students should be responsible for some portion of their college costs –even if the family can afford to pay for everything! The principal term here is "spending money." While you probably have a clear picture of what spending money is, everyone's perspective is different. The point is each family needs to sit down together and talk –to have an open and explicit talk about money. Is the expense required, optional, a luxury, etc.? Should it be suspended? All parties need to hear what the other thinks on this topic. Families need to decide whether the student needs help managing funds and making decisions about money. Define whose responsibility each expense is. Does the parent pay the cell phone bill? Does the student pay the gasoline bill? Also, discuss how to tackle"emergencies." They need to know whether or not there is ANY possibility of additional money in the future.U6venture protest preserve rejoiceprovoke renew highlight withstandstir overlook1. Although I think they overlooked their past, they would be marrying into another culture anyway since they seemed so compatible together.2. Gordon is a popular manager but he did not renew his contract with the company, which means he may leave the company soon.3. While a severe cold spread through her quivering figure, the old woman rejoiced in being free from the nightmare and the horrible memories forever.4. It is said that the party's ignorant and arrogant behavior over the years towards reserved and moderate criticism provoked the political crisis.5. Trying to convince the school that it's not her fault, the teacher protested that she should not take blame for student's cheating and that she was totally innocent.6. The difficult situation of children who were infected with HIV was highlighted Princess Diana when she presented a report to a London conference.7. All stages from eggs to adults must be capable of withstanding low environmental temperatures; eggs especially have to be cold-resistant throughout the winter.8. The government and industrial leaders were recently warned that those who even venture to think about mass layoffs were playing with fire.9. What you said must have stirred up some memories for her, days of wine and roses, nights of sufferings, wandering in the streets with intense hunger and piercing cold.。

tpo72tlp写作范文英文回答：In the dynamic realm of technological evolution, where the boundaries between human capabilities and artificial intelligence (AI) continue to blur, the question of whether AI will eventually replace human teachers in educational institutions has sparked both excitement and trepidation. While AI holds immense potential to enhance educational experiences, it is crucial to recognize its limitations and the irreplaceable role of human teachers in the complex tapestry of learning.Firstly, AI-powered systems can provide personalized learning experiences tailored to individual students' needs. By leveraging advanced machine learning algorithms and vast data sets, AI can identify areas where students struggleand adjust instruction accordingly. This customized approach can improve engagement, retention, and overall academic performance. Additionally, AI can automaterepetitive tasks such as grading, freeing up teachers' time for more meaningful interactions with students.However, it is important to acknowledge that AI alone cannot fully replicate the depth and nuance of human teaching. Teachers possess a unique combination of empathy, social intelligence, critical thinking, and cultural awareness that AI systems still lack. They can adapt to unforeseen situations, respond to students' emotional cues, and foster a positive and inclusive learning environment. Moreover, human teachers serve as role models, mentors, and guides, inspiring students to develop critical thinking skills, curiosity, and a lifelong love of learning.In a complementary future, the most effective educational approaches will likely involve a hybrid model where AI and human teachers work in tandem. AI can be leveraged to enhance certain aspects of learning, such as providing personalized feedback and automating administrative tasks, while human teachers focus on fostering essential social, emotional, and criticalthinking skills. This synergistic approach can harness thestrengths of both AI and human expertise to create a more comprehensive and effective learning environment.中文回答：人工智能在教育领域的发展引发了广泛的讨论，有人认为人工智能终将取代人类教师，但也有人认为人工智能无法完全取代人类教师的作用。

高二英语数学建模方法单选题20题1. In the process of mathematical modeling, "parameter" means _____.A. a fixed valueB. a variable valueC. a constant valueD. a random value答案：A。

解析：“parameter”常见释义为“参数”，通常指固定的值，选项 A 符合；选项B“variable value”意为“变量值”；选项C“constant value”指“常数值”；选项D“random value”是“随机值”，在数学建模中“parameter”通常指固定的值。

2. When building a mathematical model, "function" is often used to describe _____.A. a relationship between inputs and outputsB. a set of random numbersC. a single valueD. a group of constants答案：A。

解析：“function”在数学建模中常被用来描述输入和输出之间的关系，选项 A 正确；选项B“a set of random numbers”表示“一组随机数”；选项C“a single value”是“单个值”；选项D“a group of constants”指“一组常数”。

3. In the context of mathematical modeling, "optimization" refers to _____.A. finding the best solutionB. creating a new modelC. changing the parameters randomlyD. ignoring the constraints答案：A。

2Jimmy Sastra,Sachin Chitta,and Mark Yimdynamic rolling gait.Feedback was through accelerometers in the robot and an av-erage velocity of about1m/s was reported.However,this gait was not implemented on an actual robot and no analytical insight was provided.In this work,we present a new implementation of the rolling loop using sensor-based feedback.Our work differs from previous work in the use of sensory feedback, development of a simplified dynamic model that provides considerable insight for development of control and implementation on a prototype robot.Sensory feedback dramatically improves the reliability of this gait(as compared to open loop imple-mentations).The rolling loop is a closed loop system and thus hard to simulate.A complete10degree of freedom model could be built for our robot but it results in complex equations and may not provide much insight into the dynamics of the system.Further,with10actuators on the robot,the input space is big and designing controllers for such a robot is non-trivial.Our approach is to simplify the model for the system by restricting the type of controller to track an appropriate shape at touchdown,the contact of a module with the ground.In addition the method scales to any number of modules or joints in a loop.By our choice of controller,we are able to control the shape of the robot by varying a single parameter.In addition to simplifying the control algorithm,our approach also offers better insight into the dynamics of the system.This paper is structured as follows.In Section2,we present the robot used in this work.In Section3,we propose the framework used for control.In Section4 we present a simple four-bar like model for the robot.In Section5,we present theoretical results derived using this model.Experimental results are also presented in Section5.In Section6,we follow up with a discussion on insight gained from the results and possible future applications.Fig.1.(a)Kinematic Rolling(b)Dynamic Rolling:Ideal Case(c)Dynamic Rolling: Loop turns back on itself.Dynamic Rolling for a Modular Loop Robot3 2The robotThe modular robot used in this work is shown in Figure2(a).An individual module is shown in Figure2(b).Each module is made up of a hobby servo that drives a rotary degree of munication is through a global bus based on the RoboticsBus protocol[3]which is built on the CANbus standard(Controller Area Network). Control signals are provided to individual modules at60Hz.A separate add-on microcontroller board serves as a controller.It plugs into one of the ports on the robot(there are seven external and one internal ports)and provides control signals for all modules.Control is implemented by specifying a desired angular position for each servo at60Hz.This translates into a desired shape of the robot.Touchdown is detected using custom-built sensors plugged into a port on the inside of each module. The sensors used here are IR based proximity sensors that indicate distance to the ground.This information is put on the bus at60Hz.The controller determines touchdown using pre-determined thresholds for the sensors on different surfaces.(b)An individual module.(a)Football shape of a10module robot.Fig.2.The modular robot used for experiments.3Control3.1Kinematic RollingA kinematic roll is often implemented by repeatedly moving the shape of the loop such that the long axis rotates.One rotation of the long axis would be one cycle of the gait.The frequency of rotation is directly proportional to the speed,ie stopping the tread causes the whole robot to stop.For a closed loop robot like the one used in this work,one typical loop shape has two lines of modules one on top of the other attached by an intermediate set of modules as shown in Figure1(a).A kinematic roll is now executed by smoothly interpolating the position of each module to the next one in the loop.This type of motion can be easily represented using a gait table[10].3.2Dynamic RollingTo create a dynamic rolling motion,the basic approach is to move the center of mass beyond the pivot point for the module currently on the ground(Figure1(b)4Jimmy Sastra,Sachin Chitta,and Mark Yimand Figure4).This results in a moment contribution from the weight of the robot in the direction of rolling and the robot accelerates in that direction.The motion of the robot after touchdown can be separated into two phases:(1)a shape change where the robot changes shape to the new desired shape that increases the distance between the center of mass and the ground contact point and(2)a falling phase where the robot’s shape is frozen and the robot behaves essentially like an inverted pendulum pivoting about the contact point.In this paper,we will show that the first phase results in a slight deceleration while in the second phase the robot is continuously accelerating towards the next touchdown.We restrict the shape of theFig.3.Model used for analysis.robot to a shape as shown in Figure3that is formed by joining two equal arcs of a circle.In the limit,as the two arcs approach a semi-circle,the shape reduces to a circle.The modules of the robot approximate these arcs of a circle to form the desired shape in Figure3which closely resembles an American football shape.The shape can be defined using a single parameter-θa,the angle between the modules at the top and bottom apex of the shape(Figure3).All the other joint angles are equal to each other(to sayθs)and can be derived in terms ofθa using the expression 2θa+8θs=2π.Note that although the robot shown uses10modules,these two joint angles are all that are required for any number of modules.More elongated shapes(corresponding to higher values ofθa)will result in a bigger moment arm and higher angular acceleration.However,the amount of shape change(represented by the net change of joint angles)is also much higher.Rounder shapes correspond to a smaller value ofθa and will result in a smaller moment arm and smaller amount of shape change.Thus,we should expect that more elongated shapes will give us higher accelerations while rounder shapes may be more efficient.We will examine the effect of the desired shape on the speed of the robot by varying the single parameter(θa).An important point to note for this controller is that during a shape change, the joint angles for only four modules will be transitioning while the joint angles for all other modules remainfixed.We will exploit this crucial property,a consequence of choosing this particular controller,in developing a simplified model for dynamic rolling in the next section.In addition to the change of shape,another parameter that plays an important role in the gait is the speed at which this shape change is carried out.To get initial acceleration,we need to start out with afinite rate of change of shape.Choosing too high an initial rate change will cause the robot to accelerate suddenly and may result in undesirable dynamic modes where the robot falls backwards(Figure1(c)). Too low a rate may not be sufficient to get the robot started.Further,as the robotDynamic Rolling for a Modular Loop Robot5 moves faster,the shape change rate needs to be adjusted so that shape change occurs before the next touchdown happens.At higher rolling speeds of the robot,it is also beneficial to reduce the amount of shape change,ie make the desired shape rounder. Thus,we now have a discrete control algorithm applied at every touchdown that specifies two parameters:(1)the new desired shape by specifyingθa and(2)the shape change rate to converge to the desired shape.4Analytical modelTo simplify the modeling of dynamic rolling wefirst observe that only four modules are moving at a time.We can thus simplify the model of the loop to that of afloating four-bar mechanism.The two longer arcs(nodes2through5and nodes7through 10)represent two of the links of the four-bar while the other two links(comprising node1and6)are made up of single modules.This framework is shown in Figure4.Fig.4.Phases of dynamic rolling.We define a step of the gait as the sequence of events between consecutive touch-downs of two adjacent modules.At touchdown,θa is decreased toθs.This part of the step is illustrated in Figure4(b).Once it reaches the new desired position,the local shape does not deform anymore.Now,the robot undergoes a pure falling motion (Figure4(d)).The robot falls like an inverted pendulum until node3touches down on the ground(Figure4(e)).At this point,we reassign the nodes to the different links based on the global positions of the nodes.Thus,now node2forms one link for the four bar as does node7.Nodes3through6and nodes8through1comprise the other2links of the four-bar(Figure4(f)).Reducing the model in this manner manner to the one degree of freedom four bar linkage implies that the shape of the robot can be parameterized using a single parameter,the angle at the apexθa(or similarlyθs).6Jimmy Sastra,Sachin Chitta,and Mark YimThe equations of motion for this simplified version of the robot are derived using a standard method byfirst defining the Lagrangian for the system and deriving Lagrange’s equations.The generalized coordinates used in the analysis are the apex angleθa and the global angle made by the robot with the groundθg(Figure3). The mass of the modules is assumed to be0.138kg.Each module is considered to be a thin rod of length0.06m.The resultant equation for the evolution ofθg can be expressed in the form:¨θg=f1(θa,θg)mg+f2(τ).(1)Dynamic Rolling for a Modular Loop Robot7 the transition condition is given by the following momentum transfer equation on impact:L+=ηL−.5Results5.1Theoretical resultsMultiple simulations were run with different desired shapes for the robot at touch-down.We are primarily interested in two quantities in simulation:(1)The terminal velocities we can achieve with different shapes and(2)a measure of the energy ef-ficiency of the robot.Energy efficiency is measured using a quantity called specific resistance which is calculated asPǫ=8Jimmy Sastra,Sachin Chitta,and Mark YimDynamic Rolling for a Modular Loop Robot910Jimmy Sastra,Sachin Chitta,and Mark YimHowever,issues like low stiffness,higher weight and actuator limitations will hinder the performance of bigger loops.Fig.9.The motion of the robot is from right to left.References1. 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