Table Of ContentAutomata and Languages
Springer-Verlag London Ltd.
Alexander Meduna
Automata and
Languages
Theory and Applications
Springer
Alexander Meduna, PhD
Department of Computer Science and Engineering, Technical University of Brno,
Bozetechova 2, Brno 61266, Czech Republic
ISBN 978-1-85233-074-3
British Library Cataloguing in Publication Data
Meduna, Alexander
Automata and languages: theory and applications
1. Machine theory 2. Formal languages 3. Computational intelligence
I. Title
511.3
ISBN 978-1-85233-074-3
Library of Congress Cataloging-in-Publication Data
Meduna, Alexander, 1957-
Automata and languages: theory and applications / Alexander
Meduna.
p. cm.
Includes bibliographical references and index.
ISBN 978-1-85233-074-3 ISBN 978-1-4471-0501-5 (eBook)
DOI 10.1007/978-1-4471-0501-5
1. Automata. 2. Formal languages. I. Title.
QA267.M43 1999 98-52375
511.3—dc21 CIP
Apart from any fair dealing for the purposes of research or private study, o crriticism or review,
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© Springer-Verlag London 2000
Originally published by Springer-Verlag London Limited In 2000
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The publisher makes no representation, express or implied, with regard to the accuracy of the
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Typesetting: Gray Publishing, Tunbridge Wells
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In memoryofProfessor]iriKopriva
Acknowledgements
ThisbookisbasedonlecturenotesthatIuseformycomputerscienceclass
esdealingwithautomata,languages,computability,andcompilersatvarious
AmericanandEuropean universities.ItaughttheseclassesattheUniversity
ofMissouri - Columbia for almost a decade during which time I greatly
benefitedfromconversationswithmycolleaguesandstudents.Regardingthe
finalversionofthetext,Ialsoprofitedfromthesuggestionsofmycolleagues
at the Department ofComputer Science and Engineering at the Technical
UniversityofBmo.SeveralstaffmembersofSpringerprovidedhelpduring
the preparation of this book; my special thanks go to my editor,
RebeccaMowat,myproductioncontroller,JoanneCooling,andmytypesetter,
Robert Gray. Finally, I thank my wife Ivana for her support and, most
importantly,herlove.
AlexanderMeduna
Preface
Automatarepresentfundamentalabstractmodelsofcomputation.Thisbook
presentsan introduction to them.Itconcentrateson their threebasictypes
- finite automata,pushdown automata,and Turing machines.The present
textdemonstratespropertiesandpoweroftheseautomatabyexamininglan
guages thattheydefine. Besidesautomata,thisbookalso coverssomeother
modelsthatdefinelanguages;most importantly,these modelsincluderegu
lar expressions and context-freegrammars. In addition,it adapts language
modelsfortranslationsandexplainshowtoconstructcompilersbyusingthese
translation models. In itsconclusion,basedonthe results concerningmod
elsforlanguagesandtranslations,thisbookdiscussesthemostessentialtop
ics of computational theory, such as computability, decidability and
computationalcomplexity.
Organization
Thetextconsistsoffive parts:
PartIreviewsbasicmathematicalconcepts,includingsets,relation,graphs,
andprooftechniques.Inaddition,itgivesarudimentaryintroductiontothe
basicmodelsforlanguagesandcomputation.
PartIIdealswithregularlanguages.Thispartstudiestwobasicmodelsfor
these languages - regularexpressionsandfinite automata.In particular,it
establishestheequivalenceofthese modelsandexaminestheirproperties.
PartIIIexploresthefundamentalmodelsforcontext-freelanguages,name
ly,context-freegrammarsandpushdownautomata;moreover,itdefinessome
variantsofthesemodels.Thepropertiesofthesemodelsarestudiedindetail.
PartIVgoesbeyondtheclassofcontext-freelanguages.Itdefinesandinves
tigatesTuringmachines,two-pushdownautomata,andunrestrictedgrammars.
This part also presents the fundamental classification of languages, the
Chomskyhierarchy.
Part Vadapts the language models for translations.First,itobtains finite
transducers from finite automata.Then,it develops pushdown transducers
frompushdownautomata.Byusingfiniteandpushdowntransducers,apro
gramming language translator is built up. Finally, this part derives Turing
transducersfrom theTuring machines. Basedupon Turing transducers, the
text treatssuch importanttopics ofcomputational theoryas computability,
decidability,andcomputationalcomplexity.
Each ofthese parts ends with bibliographic notes,includingsuggestions
for furtherreading.
viii AutomataandLanguages
Approach
Thisbookprimarilyrepresentsatheoreticallyorientedtreatment.Asaresult,
itintroducesallformalism concerningautomatawithenoughrigortomake
all resultsquiteclearandvalid.Bypresentingmanyalgorithms,worked-out
examples,andcomputerprograms,thepresenttextalsomaintainsanemphasis
on the practical use of models for languages and translations. Most
importantly,itbuildsupacompletecompilerbyusingthem.
Exercises
At theendofeverychapter,asetofexercisesisgiven to reinforceand aug~
mentthematerialcoveredinthechapter.Exercisesarenumberedasi.j,mean
ing thejthexercise related to the material in Section i ofthe chapter.They
arelistedaccordingtolevelofdifficulty,rangingfromquitestraightforward
tomoredifficultexercises,whichareindicatedbystars.Morespecifically,singly
starredexercisescontainproblemsthatrequireonesignificantinsightfortheir
solution,anddoublystarredexercisesrequiremorethanonesuchinsight.In
addition,programmingprojectsalsoappearattheendofmostchapters.
Use
Thisbookisusefultoeverybodyinterestedinunderstandingthefundamen
tal modelsand ideas underlyingcomputation.Itcan alsobe usedasa text
bookforanintroductorycourseinautomatatheoryatjuniorandseniorlevels.
Althoughitcontainsenoughmaterialforafull yearcourse,itisalso recom
mended as the basis for a one-semester course, covering some selected
essential topics ofautomata theory. Indeed, the text provides the flexibility
neededtodesignseveralcoursesofthiskind,suchasthefollowingfivesample
one-semesterschedules.
1. Introductiontoautomata:
1.1-1.3,2.1-2.3,3.1,3.2.1-3.2.3,3.3.1.1,3.3.2-3.3.3,4.1-4.2,5.1,
5.2.1,5.2.3,5.3.1.1,5.3.2-5.3.3,6.1-6.2,7.1,7.3,8.1.1-8.1.6,8.3.1
8.3.2,8.4,9.1-9.2,10.1-10.4.
2. Finiteautomataand regularexpressions:
1.1,2.1,3.1-3.3,4.1-4.3,7.2,9.1,9.3.1.
3. Pushdownautomataand context-freegrammars:
1.1-1.3,2.1-2.2,5.1-5.3,6.1-6.3,7.1,7.3,8.2,9.2,9.3.2.
4. Introductionto compilers:
1.1-1.3,2.1-2.2,3.1,3.2.1-3.2.3,3.3,5.1.1-5.1.2,5.2-5.3,9.1-9.3.
5. Introductionto computationaltheory:
1.1-1.3,2.1-2.3,8.1-8.4,10.1-10.4.
Preface ix
Notes
Algorithms,examples,lemmas,andtheoremsarenumberedsequentiallywith
insections.Thetextalsocontainslogicalunits,suchasdefinitions.Theseunits
areconcludedbythefollowingsymbols:
Symbol Typeofunit
•
definition
•
convention
o
partofaproof
•
completeproof
L. partofanexample
.6. completeexample
Contents
PartIintrodurtion 1
MathematicalBackground 3
0.1 Sets 3
0.2 Relations 7
0.3 Graphs 11
0.4 Proofs 15
Exercises 18
Chapter1Languages 2S
1.1 Formalizationoflanguages 25
1.2 Expressionsandgrammars 33
1.2.1 Expressions 33
1.2.2 Grammars 34
1.2.3 Specificationofaprogramming language 39
1.3 Translations 48
Exercises 52
ProgrammingProjects 57
Chapter2Automata S9
2.1 Conceptualizationofautomata 59
2.2 Transducers 71
2.3 Computability 78
Exercises 82
ProgrammingProjects 88
Bibliographicnotes 90
Part II Regular Languages 91
Chapter3ModelsforRegularLanguages 93
3.1 Regularexpressions 93
3.2 Finiteautomata 99
3.2.1 Basicdefinitions 99
3.2.2 Eliminationof£-moves 122
