Finite-State Techniques: Automata, Transducers and Bimachines

315 Pages·2019·3.559 MB·English

by  Stoyan Mihov, Klaus U. Schulz

CambridgeTractsinTheoreticalComputerScience60
Finite-StateTechniques
Finite-statemethodsarethemostefficientmechanismsforanalysingtextualand
symbolicdata,providingelegantsolutionsforanimmensenumberofpractical
problemsincomputationallinguisticsandcomputerscience.
Thisbookforgraduatestudentsandresearchersgivesacompletecoverageofthe
field,startingfromaconceptualintroductionandbuildingtoadvancedtopicsand
applications.Thecentralfinite-statetechnologiesareintroducedwithmathematical
rigour,rangingfromsimplefinite-stateautomatatotransducersandbimachinesas
‘input-output’devices.Specialattentionisgiventotherichpossibilitiesof
simplifying,transformingandcombiningfinite-statedevices.
Allalgorithmspresentedareaccompaniedbyfullcorrectnessproofsandexecutable
sourcecodeinanewprogramminglanguage,C(M),whichfocusesontransparencyof
stepsandsimplicityofcode.Thus,byenablingreaderstoobtainadeepformal
understandingofthesubjectandtoputfinite-statemethodstorealuse,thisbook
closesthegapbetweentheoryandpractice.
STOYAN MIHOVisAssociateProfessorattheBulgarianAcademyofSciences
(IICT)andalectureratSofiaUniversity.Hehaspublishedseveralefficientautomata
constructionsandapproximatesearchmethods,whicharewidelyusedfornatural
languageprocessingandinformationretrieval.DrMihovhasledthedevelopmentof
multipleaward-winningsystemsforlanguageandspeechprocessing.
KLAUS U. SCHULZisProfessorofInformationandLanguageProcessingatthe
Ludwig-Maximilians-UniversitätinMunich.Hehaspublishedover100articlesin
distinctfieldsofcomputerscience,withcontributionsinapproximatesearchand
transducertechnology.Hewasheadofmanyprojectsintext-correctionanddigital
humanities,onbothanationalandEuropeanlevel.
CAMBRIDGE TRACTS IN THEORETICAL COMPUTER SCIENCE 60
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S.Abramsky,DepartmentofComputerScience,UniversityofOxford
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Finite-State Techniques
Automata, Transducers and Bimachines
STOYAN MIHOV
BulgarianAcademyofSciences
KLAUS U. SCHULZ
Ludwig-Maximilians-UniversitätMünchen
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9781108485418
DOI:10.1017/9781108756945
(cid:2)c CambridgeUniversityPress2019
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2019
PrintedandboundinGreatBritainbyClaysLtd,ElcografS.p.A.
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloging-in-PublicationData
Names:Mihov,Stoyan,1968–author.|Schulz,K.U.(KlausUlrich),1957–author.
Title:Finite-statetechniques:automata,transducersandbimachines/
StoyanMihov,KlausU.Schulz.
Description:NewYork,NY:CambridgeUniversityPress,2019.|Series:
Cambridgetractsintheoreticalcomputerscience;60
Identifiers:LCCN2019000810|ISBN9781108485418(hardback)
Subjects:LCSH:Sequentialmachinetheory.
Classification:LCCQA267.5.S4M5252019|DDC511.3/50285635–dc23
LCrecordavailableathttps://lccn.loc.gov/2019000810
ISBN978-1-108-48541-8Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof
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Contents
Preface pageix
PART I FORMAL BACKGROUND
1 FormalPreliminaries 3
1.1 Sets,FunctionsandRelations 3
1.2 LiftingFunctionstoSetsandTuples 8
1.3 Alphabets,WordsandLanguages 10
1.4 WordTuples,StringRelationsandStringFunctions 13
1.5 TheGeneralMonoidalPerspective 16
1.6 SummingUp 20
1.7 ExercisesforChapter1 21
2 MonoidalFinite-StateAutomata 23
2.1 BasicConceptandExamples 23
2.2 ClosurePropertiesofMonoidalFinite-StateAutomata 30
2.3 MonoidalRegularLanguagesandMonoidalRegular
Expressions 33
2.4 EquivalenceBetweenMonoidalRegularLanguagesand
MonoidalAutomatonLanguages 35
2.5 SimplifyingtheStructureofMonoidalFinite-StateAutomata 37
2.6 SummingUp 41
2.7 ExercisesforChapter2 41
3 ClassicalFinite-StateAutomataandRegularLanguages 43
3.1 DeterministicFinite-StateAutomata 43
3.2 DeterminizationofClassicalFinite-StateAutomata 46
3.3 AdditionalClosurePropertiesforClassicalFinite-State
Automata 48
v
vi Contents
3.4 MinimalDeterministicFinite-StateAutomataandthe
Myhill–NerodeEquivalenceRelation 50
3.5 MinimizationofDeterministicFinite-StateAutomata 57
3.6 ColouredDeterministicFinite-StateAutomata 62
3.7 Pseudo-DeterminizationandPseudo-Minimizationof
MonoidalFinite-StateAutomata 67
3.8 SummingUp 69
3.9 ExercisesforChapter3 69
4 MonoidalMulti-TapeAutomataandFinite-StateTransducers 72
4.1 MonoidalMulti-TapeAutomata 72
4.2 AdditionalClosurePropertiesofMonoidalMulti-Tape
Automata 75
4.3 ClassicalMulti-TapeAutomataandLetterAutomata 77
4.4 MonoidalFinite-StateTransducers 80
4.5 ClassicalFinite-StateTransducers 83
4.6 DecidingFunctionalityofClassicalFinite-StateTransducers 85
4.7 SummingUp 90
4.8 ExercisesforChapter4 91
5 DeterministicTransducers 94
5.1 DeterministicTransducersandSubsequentialTransducers 94
5.2 ADeterminizationProcedureforFunctionalTransducers
withtheBoundedVariationProperty 100
5.3 DecidingtheBoundedVariationProperty 108
5.4 Minimal Subsequential Finite-State Transducers:
Myhill–NerodeRelationforSubsequentialTransducers 115
5.5 MinimizationofSubsequentialTransducers 123
5.6 NumericalSubsequentialTransducers 133
5.7 SummingUp 135
5.8 BibliographicNotes 135
5.9 ExercisesforChapter5 136
6 Bimachines 138
6.1 BasicDefinitions 138
6.2 EquivalenceofRegularStringFunctionsandClassical
Bimachines 145
6.3 Pseudo-MinimizationofMonoidalBimachines 149
6.4 DirectCompositionofClassicalBimachines 151
6.5 SummingUp 156
6.6 ExercisesforChapter6 156
Contents vii
PART II FROM THEORY TO PRACTICE
7 TheC(M)language 161
7.1 BasicsandSimpleExamples 161
7.2 Types,TermsandStatementsinC(M) 168
8 C(M)ImplementationofFinite-StateDevices 177
8.1 C(M)ImplementationsforAutomataAlgorithms 177
8.2 C(M)ProgramsforClassicalFinite-StateTransducers 194
8.3 C(M)ProgramsforDeterministicTransducers 211
8.4 C(M)ProgramsforBimachines 222
9 TheAho–CorasickAlgorithm 236
9.1 FormalConstruction–FirstVersion 236
9.2 LinearComputationoftheAho–CorasickAutomaton 244
9.3 Space-Efficient Variant – Construction of the
Aho–Corasickf-Automaton 246
10 TheMinimalDeterministicFinite-StateAutomatonfora
FiniteLanguage 253
10.1 FormalConstruction 253
10.2 C(M)ImplementationoftheConstruction–FirstVersion 258
10.3 EfficientConstructionoftheMinimalDictionaryAutomaton 262
10.4 AdaptingtheLanguageofMinimalDictionaryAutomata 265
10.5 The MinimalSubsequential Transducer fora Finite
Two-SidedDictionary 270
11 ConstructingFinite-StateDevicesforTextRewriting 279
11.1 SimpleTextRewritingBasedonRegularRelations 280
11.2 UsingDeterministicMachinesforSimpleTextRewriting 282
11.3 Leftmost-LongestMatchTextRewriting 288
11.4 RegularRelationsforLeftmost-LongestMatchRewriting 290
References 298
Index 302

Preface
Finite-statetechniquesprovidetheoreticallyelegantandcomputationallyeffi-
cient solutions for various (hard, non-trivial) problems in text and natural
languageprocessing.Duetoitsimportanceinmanyfundamentalapplications,
the theory of finite-state automata and related finite-state machines has been
extensivelystudiedanditsdevelopmentstillcontinues.
This textbook describes the basics of finite-state technology, following a
combined mathematical and implementational point of view. It is written for
advanced undergraduate and graduate students in computer science, compu-
tational linguistics and mathematics. Though concepts are introduced in a
mathematically rigorous way and correctness proofs for all procedures are
given,thebookisnotmeantasapurelytheoreticalintroductiontothesubject.
Theultimategoalistobringstudentstoapositionwheretheycanbothunder-
stand and implement complex finite-state based procedures for practically
relevanttasks.Someofthespecificfeaturesofthebookarethefollowing.
1. The spectrum of finite-state machines that are covered is not restricted to
classicalfinite-stateautomataand‘recognition’tools.Wealsotreatimpor-
tant ‘input-output’ and ‘translation’ devices such as multi-tape automata,
finite-state transducers and bimachines. All these machines can be used,
forexample,forefficienttextrewriting,informationextractionfromtextual
corpora,andmorphologicalanalysis.
2. Afteraconceptualintroduction,fullimplementations/executableprograms
are given for all procedures, including a documentation of the program-
ming code. In this way it is possible to observe the concrete behaviour of
algorithms for examples selected by the readers. It is also not difficult to
enhancethegivenprogramsbymeansofself-writtentracefunctionalities,
whichhelpsevenbetterunderstandingofparticulardetailsofthealgorithms
andprogramspresented.
ix