Automata theory and its applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2001
|
| Series: | Progress in computer science and applied logic
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 403 - 421 |
| Physical Description: | XIV, 430 S. graph. Darst. : 24 cm |
| ISBN: | 3764342072 0817642072 |
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MARC
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Record in the Search Index
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| adam_text | BAKHADYR KHOUSSAINOV ANIL NERODE AUTOMATA THEORY AND ITS APPLICATIONS
BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS PREFACE XI 1 BASIC NOTIONS 1
1.1 SETS 1 1.2 SEQUENCES AND TUPLES 5 1.3 FUNCTIONS, RELATIONS,
OPERATIONS 6 1.4 EQUIVALENCE RELATIONS 11 1.5 LINEARLY ORDERED SETS 14
1.6 PARTIALLY ORDERED SETS 17 1.7 GRAPHS 19 1.8 INDUCTION 24 1.9 TREES
AND KONIG S LEMMA 27 1.10 COUNTABLE AND UNCOUNTABLE SETS 30 1.10.1
COUNTABLE SETS 32 1.10.2 DIAGONALIZATION AND UNCOUNTABLE SETS 35 1.11
ALGORITHMS 36 2 FINITE AUTOMATA 39 2.1 TWO EXAMPLES 40 2.1.1 THE
CONSUMER-PRODUCER PROBLEM 40 2.1.2 A MONKEY AND BANANA PROBLEM 42 2.2
FINITE AUTOMATA 46 VI CONTENTS 2.2.1 DEFINITION OF FINITE AUTOMATA AND
LANGUAGES 46 2.2.2 RUNS (COMPUTATIONS) OF FINITE AUTOMATA 50 2.2.3
ACCESSIBILITY AND RECOGNIZABILITY 56 2.3 CLOSURE PROPERTIES 58 2.3.1
UNION AND INTERSECTION 58 2.3.2 COMPLEMENTATION AND NONDETERMINISM 62
2.3.3 ON THE EXPONENTIAL BLOW-UP OF COMPLEMENTATION 66 2.3.4 SOME OTHER
OPERATIONS 67 2.3.5 PROJECTIONS OF LANGUAGES 70 2.4 THE MYHILL-NERODE
THEOREM 72 2.5 THE KLEENE THEOREM 76 2.5.1 REGULAR LANGUAGES 76 2.5.2
REGULAR EXPRESSIONS 79 2.5.3 THE KLEENE THEOREM 81 2.6 GENERALIZED
FINITE AUTOMATA 85 2.7 THE PUMPING LEMMA AND DECIDABILITY 93 2.7.1 BASIC
PROBLEMS 93 2.7.2 THE PUMPING LEMMA 93 2.7.3 DECIDABILITY 95 2.8
RELATIONS AND FINITE AUTOMATA 97 2.9 FINITE AUTOMATA WITH EQUATIONS 101
2.9.1 PRELIMINARIES 101 2.9.2 PROPERTIES OF ^-LANGUAGES 103 2.10 MONADIC
SECOND ORDER LOGIC OF STRINGS 105 2.10.1 FINITE CHAINS 105 2.10.2 THE
MONADIC SECOND ORDER LOGIC OF STRINGS 106 2.10.3 SATISFIABILITY 109
2.10.4 DISCUSSION AND PLAN ABOUT SFS ILL 2.10.5 FROM AUTOMATA TO
FORMULAS 112 2.10.6 FROM FORMULAS TO AUTOMATA 117 3 BIICHI AUTOMATA 121
3.1 TWO EXAMPLES 122 3.1.1 THE DINING PHILOSOPHERS PROBLEM 123 3.1.2
CONSUMER-PRODUCER PROBLEM REVISITED 125 3.2 BUCHI AUTOMATA 127 3.2.1
BASIC NOTIONS 128 3.2.2 UNION, INTERSECTION, AND PROJECTION 139 3.3 THE
BUCHI THEOREM 143 3.3.1 AUXILIARY RESULTS 143 3.3.2 BIICHI S
CHARACTERIZATION 147 3.4 COMPLEMENTATION FOR BUCHI AUTOMATA 150 3.4.1
BASIC NOTATIONS 150 CONTENTS VII 3.4.2 CONGRUENCE ~ 151 3.5 THE
COMPLEMENTATION THEOREM 154 3.6 DETERMINISM 160 3.7 MIILLER AUTOMATA 162
3.7.1 MOTIVATION AND DEFINITION 163 3.7.2 PROPERTIES OF MIILLER AUTOMATA
167 3.7.3 SEQUENTIAL RABIN AUTOMATA 170 3.8 THE MCNAUGHTON THEOREM 175
3.8.1 FLAG POINTS 175 3.8.2 THE THEOREM 179 3.9 DECIDABILITY 184 3.10
BIICHI AUTOMATA AND THE SUCCESSOR FUNCTION 187 3.10.1 W-STRINGS AS
STRUCTURES., 187 3.10.2 MONADIC SECOND ORDER FORMALISM 189 3.10.3
SATISFIABILITY 191 3.10.4 FROM BIICHI AUTOMATA TO FORMULAS 194 3.10.5
FROM FORMULAS TO BIICHI AUTOMATA 198 3.10.6 DECIDABILITY AND
DEFINABILITY IN S IS 201 3.11 AN APPLICATION OF THE MCNAUGHTON THEOREM
202 4 GAMES PLAYED ON FINITE GRAPHS 209 4.1 INTRODUCTION 209 4.2 FINITE
GAMES 210 4.2.1 INFORMAL DESCRIPTION 210 4.2.2 DEFINITION OF FINITE
GAMES AND EXAMPLES 212 4.2.3 FINDING THE WINNERS 215 4.3 INFINITE GAMES
218 4.3.1 INFORMAL DESCRIPTION AND AN EXAMPLE 218 4.3.2 FORMAL
DEFINITION OF GAMES 220 4.3.3 STRATEGIES 222 4.4 UPDATE GAMES AND UPDATE
NETWORKS 224 4.4.1 UPDATE GAMES AND EXAMPLES 225 4.4.2 DECIDING UPDATE
NETWORKS. 226 4.5 SOLVING GAMES 231 4.5.1 FORGETFUL STRATEGIES 231 4.5.2
CONSTRUCTING FORGETFUL STRATEGIES 236 4.5.3 NO-MEMORY FORCING STRATEGIES
239 4.5.4 FINDING WINNING FORGETFUL STRATEGIES 243 5 RABIN AUTOMATA 249
5.1 RABIN AUTOMATA 250 5.1.1 UNION, INTERSECTION, AND PROJECTION 259 5.2
SPECIAL AUTOMATA 262 VIII CONTENTS 5.2.1 BASIC PROPERTIES OF SPECIAL
AUTOMATA 263 5.2.2 A COUNTEREXAMPLE TO COMPLEMENTATION 265 5.3 GAME
AUTOMATA 270 5.3.1 WHAT IS A GAME? 270 5.3.2 GAME AUTOMATA 272 5.3.3
STRATEGIES 274 5.4 EQUIVALENCE OF RABIN AND GAME AUTOMATA 276 5.5
TERMINOLOGY: ARENAS, GAMES, AND STRATEGIES 281 5.6 THE NOTION OF RANK
287 5.7 OPEN GAMES . 290 5.8 CONGRUENCE RELATIONS 292 5.9 SEWING THEOREM
295 5.10 CAN MR. (E) VISIT C INFINITELY OFTEN? 300 5.10.1 DETERMINACY
THEOREM FOR GAMES (Q, [C], E) 301 5.10.2 AN EXAMPLE OF MORE COMPLEX
GAMES 304 5.11 THE DETERMINACY THEOREM 306 5.11.1 GH-GAMES AND LAST
VISITATION RECORD 306 5.11.2 THE RESTRICTED MEMORY DETERMINACY THEOREM.
308 5.12 COMPLEMENTATION AND DECIDABILITY 318 5.12.1 FORGETFUL
DETERMINACY THEOREM 318 5.12.2 SOLUTION OF THE COMPLEMENTATION PROBLEM
319 5.12.3 DECIDABILITY 327 6 APPLICATIONS OF RABIN AUTOMATA 329 6.1
STRUCTURES AND TYPES 330 6.2 THE MONADIC SECOND ORDER LANGUAGE 333 6.3
SATISFIABILITY AND THEORIES 336 6.4 ISOMORPHISMS 338 6.5 DEFINABILITY IN
T AND DECIDABILITY OF S2S 339 6.5.1 E-VALUED TREES AS STRUCTURES 340
6.5.2 DEFINABLE RELATIONS 341 6.5.3 FROM RABIN AUTOMATA TO FORMULAS 343
6.5.4 FROM FORMULAS TO RABIN AUTOMATA 346 6.5.5 DEFINABILITY AND
DECIDABILITY 349 6.6 THE STRUCTURE WITH U SUCCESSORS 350 6.7
APPLICATIONS TO LINEARLY ORDERED SETS 354 6.7.1 TWO ALGEBRAIC FACTS 354
6.7.2 DECIDABILITY 358 6.8 APPLICATION TO UNARY ALGEBRAS 361 6.8.1 UNARY
STRUCTURES 361 6.8.2 ENVELOPING ALGEBRAS 363 6.8.3 DECIDABILITY 365 6.9
APPLICATIONS TO CANTOR S DISCONTINUUM 369 CONTENTS IX 6.9.1 A BRIEF
EXCURSION TO CANTOR S DISCONTINUUM 369 6.9.2 CANTOR S DISCONTINUUM AS A
TOPOLOGICAL SPACE 372 6.9.3 EXPRESSING SUBSETS OF CD IN 525 374 6.9.4
DECIDABILITY RESULTS 378 6.10 APPLICATION TO BOOLEAN ALGEBRAS 382 6.10.1
A BRIEF EXCURSION INTO BOOLEAN ALGEBRAS 382 6.10.2 IDEALS, FACTORS, AND
SUBALGEBRAS OF BOOLEAN ALGEBRAS. . . 385 6.10.3 MAXIMAL IDEALS OF
BOOLEAN ALGEBRAS 388 6.10.4 THE STONE REPRESENTATION THEOREM 390 6.10.5
HOMOMORPHISMS OF BOOLEAN ALGEBRAS 392 6.10.6 DECIDABILITY RESULTS 397
BIBLIOGRAPHY 403 INDEX 423
|
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
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| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
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| id | DE-604.BV013927492 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:34Z |
| institution | BVB |
| isbn | 3764342072 0817642072 |
| language | English |
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| physical | XIV, 430 S. graph. Darst. : 24 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Birkhäuser |
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| series | Progress in computer science and applied logic |
| series2 | Progress in computer science and applied logic |
| spelling | Khoussainov, Bakhadyr 1961- Verfasser (DE-588)123082099 aut Automata theory and its applications Bakhadyr Khoussainov ; Anil Nerode Boston [u.a.] Birkhäuser 2001 XIV, 430 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Progress in computer science and applied logic 21 Literaturverz. S. 403 - 421 Algebra gtt Automatentheorie gtt Automates ram Formele talen gtt Logica gtt Speltheorie gtt Logik Machine theory Automatentheorie (DE-588)4003953-5 gnd rswk-swf Endlicher Automat (DE-588)4224518-7 gnd rswk-swf Automatentheorie (DE-588)4003953-5 s DE-604 Endlicher Automat (DE-588)4224518-7 s Nerode, Anil 1932- Verfasser (DE-588)119133865 aut Progress in computer science and applied logic 21 (DE-604)BV004157568 21 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009530858&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Khoussainov, Bakhadyr 1961- Nerode, Anil 1932- Automata theory and its applications Progress in computer science and applied logic Algebra gtt Automatentheorie gtt Automates ram Formele talen gtt Logica gtt Speltheorie gtt Logik Machine theory Automatentheorie (DE-588)4003953-5 gnd Endlicher Automat (DE-588)4224518-7 gnd |
| subject_GND | (DE-588)4003953-5 (DE-588)4224518-7 |
| title | Automata theory and its applications |
| title_auth | Automata theory and its applications |
| title_exact_search | Automata theory and its applications |
| title_full | Automata theory and its applications Bakhadyr Khoussainov ; Anil Nerode |
| title_fullStr | Automata theory and its applications Bakhadyr Khoussainov ; Anil Nerode |
| title_full_unstemmed | Automata theory and its applications Bakhadyr Khoussainov ; Anil Nerode |
| title_short | Automata theory and its applications |
| title_sort | automata theory and its applications |
| topic | Algebra gtt Automatentheorie gtt Automates ram Formele talen gtt Logica gtt Speltheorie gtt Logik Machine theory Automatentheorie (DE-588)4003953-5 gnd Endlicher Automat (DE-588)4224518-7 gnd |
| topic_facet | Algebra Automatentheorie Automates Formele talen Logica Speltheorie Logik Machine theory Endlicher Automat |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009530858&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004157568 |
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