Automata Theory and Formal Languages (2022) [Homenda Pedrycz] [9783110752274]

246 Pages·2022·2.231 MB·

by  Homenda Pedrycz

WładysławHomenda,WitoldPedrycz
AutomataTheoryandFormalLanguages
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Władysław Homenda, Witold Pedrycz
Automata Theory
and Formal
Languages
|
Authors
Prof.WładysławHomenda Prof.WitoldPedrycz
WarsawUniversityofTechnology UniversityofAlberta
FacultyofMathematicsand Dept.ofElectrical&
InformationScience ComputerEngineering
ul.Koszykowa75 ECERFBuilding
00-662Warsaw EdmontonT6R2V4
Poland Canada
UniversityofInformationTechnologyand PolishAcademyofSciences
Management SystemsResearchInstitute
FacultyofAppliedInformationTechnology ul.Newelska6
ul.Sucharskiego2 01-447Warsaw
35-225Rzeszów Poland
Poland [email protected]
[email protected]
ISBN978-3-11-075227-4
e-ISBN(PDF)978-3-11-075230-4
e-ISBN(EPUB)978-3-11-075231-1
LibraryofCongressControlNumber:2021947389
BibliographicinformationpublishedbytheDeutscheNationalbibliothek
TheDeutscheNationalbibliothekliststhispublicationintheDeutscheNationalbibliografie;
detailedbibliographicdataareavailableontheInternetathttp://dnb.dnb.de.
©2022WalterdeGruyterGmbH,Berlin/Boston
Coverimage:Suebsiri/iStock/GettyImagesPlus
Typesetting:VTeXUAB,Lithuania
Printingandbinding:CPIbooksGmbH,Leck
www.degruyter.com
Foreword
WhatisAutomataTheoryandwhatareitsrelationstoformallanguages?Whatcan
theydo?Howdotheywork?Howcanoneusethem?ThisexcellentbookbyWładysław
HomendaandWitoldPedryczprovidesthereaderasystematicentrypathintothean-
swersofthosequestions.Everyefforthasbeenmadetoproduceamanuscriptthat
isveryeasilyunderstood,withoutoversimplificationofthesubjectmatter.Hereisa
clear,step-by-stepIntroductiontoFormalLanguagesandAutomataTheoryaddress-
ingthemostimportantelementsinthefield.
Toviewthedevelopmentsinthisfield,abitofpersonalhistoryisinorder.When
SamLeeandIwroteourbook“FuzzySwitchingandAutomata:TheoryandApplica-
tions”in1979,ourexpectationwastheapplicabilityofthecontents.However,itisthe
seminalworkofmanyresearcherssincethenthatshowedhowAutomataTheoryand
FormalLanguagescouldbetranslatedintoaworkingreality.Itiswithinthepastfew
yearsthatithasbecomeincreasinglyclearthatasymbioticrelationshipbetweenthis
fieldandAI,forexample,aswellwithavarietyoftechniquesfromUncertaintyMan-
agementcanbeexploitedtoconceive,design,andbuildsystemsandproductshaving
highMIQ(MachineIntelligenceQuotient).
Viewedwiththoserecentdevelopments,theimportanceofthepresentmanuscript
is easily understood. Professors Homenda and Pedrycz have assembled an impres-
siveauthoritativetreatmentofsomeofthebasicissuesarisinginthefield.Professors
Homenda and Pedrycz deserve much credit as well as our congratulations on pro-
ducinganexcellenttextwithauthority,originality,andskill,whichmakethisworka
pleasuretostudyandread,anditisonlymyhopethatthisoutstandingtextwillserve
asanimpetusforcontinuedinterestinthestudyandresearchinthisexcitingfield.
Tampa,Florida,September11,2021 AbrahamKandel
https://doi.org/10.1515/9783110752304-201

Preface
Automatatheoryandformallanguagesarethecornerstoneofcomputerscienceand
allinformationprocessingpursuits.Thesefundamentalsareatthecenterofanycom-
puterscience,computerengineeringandinformationtechnologiescurriculum.Writ-
ingatextbookinthisareaisachallengingendeavor.Theareaiswellestablishedyet
theongoingtechnologicaltrendsandtheadvancementsinapplicationareascallfora
creativeexposureofthefundamentalmaterial.Thistextbookisaimedatstudentsin
senioryearsofundergraduateprogramsandthefirstyearofgraduateprograms(both
attheMScandPhDlevel).
Whenwritingthistext,westrivedforasystematicandclearexposureofthekey
ideasbypositioningtheminthecontextoftheoverallpictureandaspectrumofpos-
sibleapplications.
There are several outstanding features that will appeal to a broad spectrum of
instructorsandstudents,whichmakesthistextuniqueincomparisonwiththebooks
availableonthemarket:
(i) material is prudently selected to cater to a spectrum adequate for course well
adoptedbytheaudience;
(ii) materialismadeself-containedandmotivated;
(iii)thelengthofthetextmakesitidealforaone-semestercoursebyfocusingonthe
requiredwell-structuredandmotivatedideas;
(iv) in-depthexplanationsupportedbyawealthofsolvedexamplesandproblems;
(v) asystematicexposureofthematerial;
(vi) easyexpansionfacilitatingtheusageofthetextinavarietyofcourses.
Thetextbookcouldbealsoregardedasasoundandsystematicprerequisitetomore
advancedsubjectsintheareasofadvancedalgorithms,computabilityandcomputa-
tionalcomplexity.
Thebookisstructuredintothreepartsprecededwithallrequiredprerequisites
offeringaconciseandfocusedbackgroundtomaketheexposureofthematerialself-
contained.ThethreemainpartsarestructuredtoreflecttothegeneralChomskyhier-
archyoflanguages,namely:
(i) we start from the class of regular languages forming the simplest class of sim-
plestlanguages,andthenmovetowardtheclassofrecursivelyenumerablelan-
guages,themostcomplexclassoflanguages(Chapters2,3and4).Wecovertools
thatgeneratelanguages:regularexpressionsandregulargrammars(Chapter2),
context-freegrammars(Chapter3)andcontext-sensitiveandunrestrictedgram-
mars(Chapter4);
(ii) wegobacktotheChomskyhierarchybystudyingtoolsusedtoacceptlanguages
startingfromthemostcomplexclassoflanguagesandendingwiththesimplest
classoflanguages(Chapters5,6and7).HereconsideredareTuringmachineswith
https://doi.org/10.1515/9783110752304-202
VIII | Preface
theirdiversecategories,Turingmachineswithstoppropertyandlinearbounded
automata,whichacceptrecursivelyenumerablelanguages,recursivelanguages
and context-sensitive languages (Chapter 5). Then we discuss push-down au-
tomata,whichacceptcontext-freelanguages(Chapter6).Finally,westudyfinite
automata,whichacceptregularlanguages(Chapter7);
(iii)finally,werevisitbothpathsbyunifyingtoolstogenerateandacceptlanguages
(Chapters8and9).
Figure. Organizationofthematerial.
Thetextisstructuredinawayitdeliversagreatdealofflexibilityandmakesthema-
terialsuitableforabroadspectrumofpossiblecoursesdependingupontheaudience
andtheassumedpositionofthecourseinthecurriculum.Theroadmapshowninthe
figureabovedisplaysanumberofpossibilitieshighlightinghowthematerialcouldbe
covered:
(i) Chapters2–7areindependentfromeachother;thereadercanstudyselectedones
inanyorder.Ingeneral,minorlinkagesbetweenChapters2–4andbetweenChap-
ters5–7arenotdetrimentaltotheindividualstudies;
(ii) Chapters8and9requirethemasteryoftheknowledgeofpreviouschaptersforall
ofthem.
It is worth to drawattention to Chapter 5, wherethe concept of nondeterminism is
introducedandextensivelydiscussed.Thisconceptistheonlyobstacleprerequisite
tostudysometopicscoveredinChapters6and7.
Whiletheexposedofthematerialisself-contained,weassumesomefamiliarity
ofbasicconceptsandmethodsofalgebra,settheoryandlogicandalgorithmsand
datastructures.TheseconceptsareincludedinChapter1.Itisrecommendedtorevise
theseconceptspriortostudyingtheremainingparts.
Preface | IX
Wehopethatthetextbookwillappealtoabroadaudienceofundergraduateand
graduatestudentsandallofthoseinterestedinthesystematicandconciseexposure
tothefundamentalsofautomataandformallanguages.
Edmonton,Warsaw,August2021 WładysławHomenda
WitoldPedrycz