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Afirststeptowardsaframeworkfortheautomated

analysisoffeaturemodels

DavidBenavides,SergioSegura,PabloTrinidad,AntonioRuiz-Cort´es

Dpto.ofComputerLanguagesandSystems

UniversityofSeville

{benavides,sergio,trinidad,aruiz}@tdg.lsi.us.es

Abstract—Featuremodellingisacommonmechanismforvariabilitymanagementinthecontextofsoftwareproductlines.Afteryearsofprogress,thenumberofproposalstoautomaticallyanalysefeaturemodelsisstillmodestandthedataabouttheperformanceofthedifferentsolversandlogicrepresentationsusedinsuchareaarepracticallynon–existent.ThreeofthemostpromisingproposalsfortheautomatedanalysisoffeaturemodelsarebasedonthemappingoffeaturemodelsintoCSP,SATandBDDsolvers.Inthispaperwepresentaperformancetestbetweenthreeoff-the-shelfJavaCSP,SATandBDDsolverstoanalysefeaturemodelswhichisanovelcontribution.Inaddition,weconcludethattheintegrationofsuchproposalsinaframeworkwillbeakeychallengeinthefuture.

IndexTerms—SoftwareProductLines,VariabilityManage-ment,FeatureModels.

I.INTRODUCTION

FeatureModels(FMs)areoneofthemostcommonvari-

abilitymechanisms.Goodtoolsupportisneededtodebug,

extractinformationandinsummaryanalyzeFMsinorderto

selectthemasavariabilitymechanisminaSoftwareProduct

Line(SPL)approach.AFMrepresentsallpossibleproducts

ofaSPLinasinglemodelusingfeatures.FMscanbeusedin

differentstagesofdevelopmentsuchasrequirementsengineer-

ing[10],[11],architecturedefinitionorcodegeneration[1],

[3].AFMisatree–likestructureandconsistsof:i)relations

betweenaparentfeatureanditschildfeatures.ii)cross–tree

constraintsthataretypicallyinclusionorexclusionstatements

oftheform“iffeatureFisincluded,thenfeatureXmustalso

beincluded(orexcluded)”.

AutomatedanalysisofFMsisanimportantchallengein

SPLresearch[1],[2].Itcanbeperformedusingoff–the–

shelfsolverstoautomaticallyextractusefulinformationof

theSPLsuchasthenumberofpossiblecombinationsof

features,alltheconfigurationsfollowingacriteria,finding

theminimumcostconfiguration,etc.Althoughtherehave

beensomepromisingproposalsbasedintherepresentation

ofFMsasaConstraintSatisfactionProblem(CSP),boolean

SATisfiabilityproblem(SAT)andBinaryDecisionDiagrams

(BDD)theperformanceofthesolversworkingwithsuch

representationsisunknownfortheSPLcommunity.

Inapreviouswork,wepresentedaperformancecomparison

oftwoCSPjavasolversanalysingFMs[8].Inthispaperwego

furtherintegratingdifferentsolversandlogicrepresentations.

Firstwegiveacompletemappingforthethreesolvers(BDD,

SATandCSP)andthenwepresentaperformancecomparisonofthem.Tothebestofourknowledge,thisisthefirsttestthat

measurestheperformanceofsolversdealingwithdifferent

logicrepresentationsofFMs.

Theremainderofthepaperisstructuredasfollows:in

SectionIItheautomatedanalysisofFMsisoutlinedand

detailsonhowtotranslateaFMintoaCSP,BDDandSATare

presented.SectionIIIfocusesontheresultsoftheexperiment.

Finallywesummarizeourconclusionsanddescribeourfuture

workinSectionIV.

II.AUTOMATEDANALYSISOFFEATUREMODELS

OnceaFMistranslatedintoasuitablerepresentationitis

possibletouseoff–the–shelfsolverstoautomaticallyperform

agreatvarietyofoperationssuchascalculatingthenumber

ofpossiblecombinationsoffeatures,retrievingconfigurations

followingacriteria,findingtheminimumcostconfiguration,

etc[6].

Thereisagreatvarietyoftechniquesandtoolsthatcanbe

usedintheautomatedanalysisofFMs.Thispaperfocuson

threewellknownproblemsintheareaofautomatedreasoning:

ConstraintSatisfactionProblems(CSP),BooleanSatisfiability

Problems(SAT)andBinaryDecisionDiagrams(BDD).All

thoserepresentationshavenotbeenyetfullyadoptedinthe

automatedanalysisofFMs.Inthenextsectionswewillgive

abriefoverviewofeachofthemandfinallywewillintroduce

howtranslatingaFMintoaCSP,SATandBDD.

A.ConstraintSatisfactionProblem

ConstraintProgrammingcanbedefinedasthesetoftech-

niquessuchasalgorithmsorheuristicsthatdealwithCSPs.

ACSPconsistsonasetofvariables,finitedomainsforthose

variablesandasetofconstraintsrestrictingthevaluesof

thevariables.ACSPissolvedbyfindingstates(valuesfor

variables)inwhichallconstraintsaresatisfied.CSPsolvers

candealwithnumericalvaluessuchasintegerdomains.The

mainideasconcerningtheuseofconstraintprogrammingon

FManalysiswerestatedin[6],[7].

B.BooleanSatisfiabilityProblem(SAT)

Apropositionalformulaisanexpressionconsistingona

setofbooleanvariables(literals)connectedbylogicopera-

tors(¬,∧,∨,→,↔).Thepropositionalsatisfiabilityproblem

(SAT)consistsondecidingwhetheragivenpropositional2

formulaissatisfiable,thatis,iflogicalvaluescanbeassigned

toitsvariablesinawaythatmakestheformulatrue.

Theproblemisrestrictedbyusingthepropositionalformu-

lasinconjunctivenormalform(CNF),thatis,propositional

formulascomposedbyaconjunctionofclausesinwhicheach

clauseisadisjunctionofliterals(e.g.((L1∨L2)∧(L3∨L4)∧

(L5∨L6))).Everypropositionalformulacanbeconvertedinto

anequivalentformulainCNFbyusinglogicalequivalences.

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Analysis

Analysis

Analysis: China's economic slowdown

The 2014-12-01 10:56 China investment network - A + A

Core tip: "the new normal is a global phenomenon, in fact, the Chinese academy of social

sciences, division, vice President of the committee members' think so.

The new normal is a global phenomenon

The international financial crisis over is known as the "great stability" old normal phase

"The new normal in fact is a global phenomenon", the Chinese academy of social

sciences, division, vice President of the committee members' think so.

', 'said the new normal, before the world was on a economics called "great stability" old

normal phase, since the mid - 1980 to 2007, lasted for over 20 years. "Big stable period,

the global economy has experienced a rare good times. Sustained economic growth, low

inflation and low unemployment rate, at the same time, the characteristics of the economic

Analysis of Santiago in the Old Man and the Sea 《老人与海》中圣地亚哥形象分析

Analysis of Santiago in the Old Man and the Sea 《老人与海》中圣地亚哥形象分析

i Analysis of Santiago in the Old Man and the Sea

Abstract: The Old Man and the Sea ，one of Ernest Hemingway’s most famous

work,was published in 1952.Critics praise that the novel is Hemingway’s last major

work of fiction,and he won 1953’s Pulitzer Prize for Fiction and Award of Merit

Medal from the American Academy of Letters.[1] It is a short novel，a fable of a

kind ，about an kind Cuban fisherman Santiago and his battle with a great mailin。For

84 days，Santiago does not catch a single fish but he does not feel discouraged ，He

goes far out into the sea and he hooks a giant marlin.A desperate struggle

ensues .Santiago manages to kill the fish and ties it to his boat,only to find that on the

way home he has to fight a more desperate struggle with some dangerous giant

sharks,which eat up the marlin,leaving only a skeleton .The old man brings it home

Analysis of the students

Analysis of the students

1 Analysis of the students

The students of Grade2 have got certain listening ability, which still needs well

improving. And their speaking ability is not as good as expected, which will be improved in

this period through some exercise.

Analysis of the book

1) Status and function of

the teaching material

This period will arouse the students’ interest in creating something useful. With the

interest they will learn to express and support an opinion.

2) Teaching aims

Knowledge goal

Lead the students to imagine things they would like to invent and express their thoughts

on such new inventions.

Moral goal

Lead the students to get an idea of the qualities an inventor must have, such as

imagination, bravery, perseverance.

。。。。。。。。。。。。。2 Analysis of the learners

• The students in my class are of different levels so I should adapt the lesson to each

permutation multivariate analysis of variance 解析说明

permutation multivariate analysis of variance 解析说明

permutation multivariate analysis of variance 解析说明

1. 引言

1.1 概述

在统计学领域，多元方差分析（Multivariate Analysis of Variance, MANOVA）是一种用于比较两个或多个组之间均值是否具有显著差异的统计方法。传统的MANOVA假设数据满足正态性、方差齐性和协方差矩阵齐性等假设条件。然而，当数据不满足这些假设时，传统的MANOVA会失效，因此需要使用其他替代方法。

本文将重点讨论一种替代方法——排列多元方差分析（Permutation

Multivariate Analysis of Variance, PERMANOVA）。PERMANOVA通过基于观察到的样本排列进行总体均值比较，并利用置换检验来评估组间差异是否显著。相对于传统MANOVA，PERMANOVA在数据分析中更加灵活与适应性强。

1.2 文章结构

本文将按照以下结构进行论述：

- 第1部分为引言部分，对文章内容进行概述，并介绍排列多元方差分析的背景和意义。

- 第2部分为排列多元方差分析解析部分，主要涵盖其基本概念、方法和步骤以及数学原理的详细说明。

- 第3部分将探讨排列多元方差分析在不同领域中的应用，包括社会科学、医学研究和生态学研究等。

- 第4部分将对排列多元方差分析的优势与局限性进行深入分析，并探讨其结果解释的影响因素。

- 最后，第5部分总结全文，回顾研究内容，并展望排列多元方差分析在未来的发展趋势。

1.3 目的

本文旨在全面解析排列多元方差分析（PERMANOVA），从介绍基本概念到详细说明方法与步骤，探讨其数学原理以及重要性。同时，还将通过案例和实际应用领域来阐述PERMANOVA在社会科学、医学研究和生态学研究等领域中的具体应用。此外，在总结优势与局限性时，将重点关注其 解决传统MANOVA假设条件限制 的优势，并分析结果解释受何种因素影响。最后，展望未来针对PERMANOVA方法改进和发展的可能性。