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Infinite words: automata, semigroups, logic and games

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Bibliographische Detailangaben
Beteiligte Personen:	Perrin, Dominique 1946- (VerfasserIn), Pin, Jean Éric (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Amsterdam u.a. Elsevier Acad. Pr. 2004
Ausgabe:	1. ed.
Schriftenreihe:	Pure and applied mathematics 141
Schlagwörter:	Automatentheorie - Halbgruppe - Mathematische Logik - Spieltheorie Gruppentheorie Automatentheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010744405&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XI, 538 S. graph. Darst.
ISBN:	0125321112

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Datensatz im Suchindex

DE-BY-TUM_call_number	0040 74.2004 A 2059 0102 DAT 550f 2001 A 37233
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adam_text	INFINITE WORDS AUTOMATA, SEMIGROUPS, LOGIC AND GAMES DOMINIQUE PERRIN AND JEAN-ERIC PIN UNIVERSITE DE MARNE-LA-VALLEE, FRANCE AND CNRS, UNIVERSITE PARIS VII, FRANCE ELSEVTER ACADEMIC PRESS AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO CONTENTS PREFACE 1 I. AUTOMATA AND INFINITE WORDS 5 1. INTRODUCTION 5 2. WORDS AND TREES 6 3. RATIONAL SETS OF INFINITE WORDS 13 4. AUTOMATA 16 5. BIICHI AUTOMATA 25 6. DETERMINISTIC BIICHI AUTOMATA 31 7. MULLER AND RABIN AUTOMATA 35 7.1. MULLER AUTOMATA 35 7.2. RABIN AUTOMATA 39 7.3. MULLER AUTOMATA WITH A FULL TABLE 41 8. TRANSITION AUTOMATA 43 9. MCNAUGHTON S THEOREM 45 10. COMPUTATIONAL COMPLEXITY ISSUES 60 10.1. FROM (W-RATIONAL EXPRESSIONS TO BIICHI AUTOMATA AND BACK 61 10.2. FROM MULLER AUTOMATA TO W-RATIONAL EXPRESSIONS 62 10.3. FROM BIICHI AUTOMATA TO RABIN AUTOMATA 62 10.4. FROM RABIN AUTOMATA TO MULLER AUTOMATA 63 10.5. FROM RABIN AUTOMATA TO BIICHI AUTOMATA 63 10.6. FROM STREETT AUTOMATA TO BIICHI AUTOMATA 64 10.7. COMPLEXITY OF ALGORITHMS ON AUTOMATA 65 11. EXERCISES 67 11.1. WORDS AND TREES 67 VI CONTENTS 11.2. RATIONAL SETS 67 11.3. BUCHI AUTOMATA 68 11.4. DETERMINISTIC BIICHI AUTOMATA 68 11.5. MULLER AUTOMATA 69 11.6. MCNAUGHTON S THEOREM 71 12. NOTES 71 II. AUTOMATA AND SEMIGROUPS 75 1. INTRODUCTION 75 2. RAMSEYAN FACTORIZATIONS AND LINKED PAIRS 77 2.1. RAMSEYAN FACTORIZATIONS 77 2.2. LINKED PAIRS 79 2.3. ULTIMATE CLASSES 82 2.4. IDEMPOTENT LINKED PAIRS 85 3. RECOGNITION BY MORPHISM 86 3.1. SEMIGROUP MORPHISMS 86 3.2. MORPHISMS OF ORDERED SEMIGROUPS 88 3.3. CONGRUENCE AND SYNTACTIC ORDER 90 3.4. RESIDUALS 91 4. SEMIGROUPS AND INFINITE PRODUCTS 92 4.1. & -SEMIGROUPS 92 4.2. MORPHISMS OF & -SEMIGROUPS 93 4.3. FREE STRUCTURES 95 5. WILKE ALGEBRAS 97 6. RECOGNITION BY MORPHISM OF ^-SEMIGROUPS 101 7. THE TWO MODES OF RECOGNITION 105 8. SYNTACTIC CONGRUENCE 111 9. BACK TO MCNAUGHTON S THEOREM 117 10. PROPHETIC AUTOMATA 122 11. EXERCISES 128 11.1. RAMSEYAN FACTORIZATIONS 128 11.2. RECOGNITION BY MORPHISM 129 11.3. WILKE ALGEBRAS 129 11.4. THE TWO MODES OF RECOGNITION 129 11.5. SYNTACTIC CONGRUENCE 129 11.6. BACK TO MCNAUGHTON S THEOREM 130 11.7. PROPHETIC AUTOMATA 130 12. NOTES 130 III. AUTOMATA AND TOPOLOGY 1. INTRODUCTION CONTENTS YII 2. TOPOLOGICAL SPACES 134 2.1. COUNTABLE SETS 134 2.2. GENERAL TOPOLOGY 136 2.3. METRIC SPACES 137 2.4. POLISH SPACES 140 2.5. BOREL SETS 141 3. THE SPACE OF INFINITE WORDS 144 3.1. THE TOPOLOGY OF A W 144 3.2. CLOSED SETS 146 3.3. CLOPENSETS 149 3.4. THE SECOND LEVEL OF THE BOREL HIERARCHY 150 3.5. COMPACTNESS 152 3.6. THE BOREL HIERARCHY OF A 10 154 4. THE SPACE OF FINITE OR INFINITE WORDS 157 5. BOREL AUTOMATA 164 6. SUSLIN SETS 168 7. THE SEPARATION THEOREM 177 8. EXERCISES 180 8.1. TOPOLOGICAL SPACES 180 8.2. THE SPACE OF INFINITE WORDS 180 8.3. THE SPACE OF FINITE OR INFINITE WORDS 181 8.4. BOREL AUTOMATA 184 9. NOTES 185 IV. GAMES AND STRATEGIES 187 1. INTRODUCTION 187 2. INFINITE GAMES 188 3. BOREL GAMES 190 3.1. OPEN GAMES 190 3.2. N 2 -GAMES 191 3.3. MARTIN S THEOREM 192 4. GAMES ON GRAPHS 196 4.1. SIMPLE GAMES 198 4.2. WINNING CONDITIONS 199 4.3. PARITY GAMES 202 4.4. PARITY AUTOMATA 203 4.5. RATIONAL WINNING STRATEGIES 205 5. WADGE GAMES 207 5.1. WADGE LEMMA 208 5.2. RATIONAL REDUCTION 208 6. EXERCISES 210 VIII CONTENTS 6.1. BOREL GAMES 210 6.2. INFINITE GAMES 210 6.3. GAMES ON GRAPHS 211 7. NOTES 212 V. WAGNER HIERARCHY 215 1. INTRODUCTION 215 2. ORDINALS 216 3. CLASSES OF SETS 219 3.1. WADGE CLASSES 219 3.2. THE BOOLEAN HIERARCHY 219 3.3. SEPARATED AND BISEPARATED UNION 221 4. CHAINS 223 4.1. CHAINS IN AUTOMATA 223 4.2. CHAINS IN W-SEMIGROUPS 224 4.3. CHAINS IN FINITE AI-SEMIGROUPS 225 4.4. EQUIVALENCE OF THE DEFINITIONS OF CHAINS 228 4.5. THE CHAIN HIERARCHY 230 5. SUPERCHAINS 234 5.1. SUPERCHAINS IN AUTOMATA 235 5.2. SUPERCHAINS IN & -SEMIGROUPS 236 5.3. SUPERCHAINS IN FINITE W-SEMIGROUPS 238 5.4. EQUIVALENCE OF THE DEFINITIONS OF SUPERCHAINS 241 5.5. THE SUPERCHAIN HIERARCHY 242 6. THE WAGNER HIERARCHY 250 6.1. THE DERIVED AUTOMATON 250 6.2. THE WAGNER HIERARCHY 253 6.3. BISEPARATED DIFFERENCES 254 6.4. THE STANDARD REPRESENTATIVES 256 7. EXERCISES 259 7.1. CLASSES OF SETS 259 7.2. CHAINS 260 7.3. WAGNER HIERARCHY 262 8. NOTES 263 VI. VARIETIES 265 1. INTRODUCTION 265 2. VARIETIES OF FINITE OR INFINITE WORDS 267 2.1. VARIETIES OF CO-SEMIGROUPS 267 2.2. IDENTITIES 268 2.3. THE VARIETIES THEOREM 268 CONTENTS IX 3. VARIETIES AND TOPOLOGY 272 4. WEAK RECOGNITION 277 4.1. WEAK RECOGNITION BY A MORPHISM OF ORDERED SEMIGROUPS 277 4.2. RECOGNITION VERSUS WEAK RECOGNITION 283 4.3. PROPERTIES OF THE STRONG EXPANSION 286 5. EXTENSIONS OF MCNAUGHTON S THEOREM 291 6. VARIETIES CLOSED UNDER APERIODIC EXTENSION 295 7. CONCATENATION HIERARCHIES FOR INFINITE WORDS 296 8. EXERCISES 303 8.1. VARIETIES OF FINITE OR INFINITE WORDS 303 8.2. VARIETIES AND TOPOLOGY 303 8.3. WEAK RECOGNITION 304 8.4. BOOLEAN COMBINATIONS OF DETERMINISTIC SETS 304 8.5. VARIETIES CLOSED UNDER APERIODIC EXTENSION 305 9. NOTES 305 VII. LOCAL PROPERTIES 307 1. INTRODUCTION 307 2. WEAK RECOGNITION 308 3. LOCAL PROPERTIES OF INFINITE WORDS 312 3.1. PROPERTIES DEFINED BY LETTERS 312 3.2. PREFIXES AND SUFFIXES OF INFINITE WORDS 314 3.3. FACTORS OF INFINITE WORDS 319 4. EXERCISES 324 4.1. LOCAL PROPERTIES OF FINITE WORDS 324 4.2. FACTORS OF INFINITE WORDS 324 5. NOTES 326 VIII. AN EXCURSION INTO LOGIC 327 1. INTRODUCTION 327 2. THE FORMALISM OF LOGIC 329 2.1. SYNTAX 329 2.2. SEMANTICS 332 2.3. LOGIC ON WORDS 336 3. MONADIC SECOND-ORDER LOGIC ON WORDS 340 4. FIRST-ORDER LOGIC OF THE LINEAR ORDER 346 4.1. FIRST ORDER AND STAR-FREE SETS 346 4.2. LOGICAL HIERARCHY 348 5. FIRST-ORDER LOGIC OF THE SUCCESSOR 356 5.1. FRAI SSE-EHRENFEUCHT GAMES 356 5.2. CHARACTERIZATION OF F (S) 359 CONTENTS 6. TEMPORAL LOGIC 363 6.1. ANOTHER CHARACTERIZATION OF STAR-FREE SETS 365 6.2. STAR-FREE SETS AND TEMPORAL LOGIC 369 7. RESTRICTED TEMPORAL LOGIC 373 8. EXERCISES 376 8.1. THE FORMALISM OF LOGIC 376 8.2. MONADIC SECOND-ORDER LOGIC ON WORDS 376 8.3. FIRST-ORDER LOGIC OF THE LINEAR ORDER 377 8.4. FIRST-ORDER LOGIC OF THE SUCCESSOR 377 8.5. TEMPORAL LOGIC 378 9. NOTES 378 IX. BI-INFINITE WORDS 381 1. INTRODUCTION 381 2. BI-INFINITE WORDS 382 3. DETERMINISM 390 4. MORPHISMS 395 5. UNAMBIGUOUS AUTOMATA ON BI-INFINITE WORDS 400 6. DISCRIMINATION 406 7. LOGIC ON Z 409 8. EXERCISES 410 8.1. BI-INFINITE WORDS 410 8.2. MORPHISMS 411 8.3. DISCRIMINATION 411 8.4. LOGIC ON Z 411 9. NOTES 412 X. INFINITE TREES 413 1. INTRODUCTION 413 2. FINITE AND INFINITE TREES 414 3. TREE AUTOMATA 417 3.1. AUTOMATA ON FINITE TREES 417 3.2. BIICHI TREE AUTOMATA 419 3.3. MULLER TREE AUTOMATA 420 3.4. RABIN BASIS THEOREM 424 4. TREE AUTOMATA AND GAMES 425 4.1. AUTOMATON AND PATHFINDER 426 4.2. RABIN S TREE THEOREM 427 4.3. A SECOND PROOF OF RABIN S BASIS THEOREM 428 5. TOPOLOGY 428 5.1. THE TOPOLOGICAL SPACE OF INFINITE TREES 428 CONTENTS XI 5.2. SUSLINSETS 429 5.3. RECOGNIZABLE SETS 430 6. MONADIC SECOND ORDER LOGIC OF TWO SUCCESSORS 430 7. EFFECTIVE ALGORITHMS 432 8. EXERCISES 433 9. NOTES 434 ANNEX A. FINITE SEMIGROUPS 435 1. MONOIDS, SEMIGROUPS AND SEMIRINGS 435 1.1. DEFINITIONS 435 1.2. CONGRUENCES 438 1.3. STRUCTURE OF FINITE SEMIGROUPS 441 2. GREEN RELATIONS 443 3. TRANSFORMATION SEMIGROUPS 448 4. SEMIDIRECT PRODUCT AND WREATH PRODUCT 451 4.1. DEFINITIONS 451 4.2. BASIC DECOMPOSITION RESULTS 453 5. THE WREATH PRODUCT PRINCIPLE 458 5.1. SEQUENTIAL FUNCTIONS 458 5.2. SETS RECOGNIZED BY WREATH PRODUCTS 460 6. NOTES 463 ANNEX B. VARIETIES OF FINITE SEMIGROUPS 465 1. VARIETIES OF ALGEBRAS 465 1.1. BIRKHOFF VARIETIES 465 1.2. VARIETIES OF FINITE SEMIGROUPS 468 1.3. PROFINITE ALGEBRAS 469 2. THE VARIETY THEOREM 475 3. SOME EXAMPLES OF VARIETIES 477 4. STAR-FREE SETS 481 4.1. CONCATENATION HIERARCHIES 486 4.2. VARIETIES CLOSED UNDER MARKED PRODUCT 492 5. LOCAL PROPERTIES OF FINITE WORDS 492 5.1. PREFIXES AND SUFFIXES OF FINITE WORDS 493 5.2. FACTORS OF FINITE WORDS 495 6. NOTES 498 REFERENCES 499 LIST OF TABLES 523 LIST OF FIGURES 525 INDEX 531
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illustrated	Illustrated
indexdate	2024-12-20T11:24:36Z
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isbn	0125321112
language	English
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physical	XI, 538 S. graph. Darst.
publishDate	2004
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publisher	Elsevier Acad. Pr.
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series	Pure and applied mathematics
series2	Pure and applied mathematics
spellingShingle	Perrin, Dominique 1946- Pin, Jean Éric Infinite words automata, semigroups, logic and games Pure and applied mathematics Automatentheorie - Halbgruppe - Mathematische Logik - Spieltheorie Gruppentheorie (DE-588)4072157-7 gnd Automatentheorie (DE-588)4003953-5 gnd
subject_GND	(DE-588)4072157-7 (DE-588)4003953-5
title	Infinite words automata, semigroups, logic and games
title_auth	Infinite words automata, semigroups, logic and games
title_exact_search	Infinite words automata, semigroups, logic and games
title_full	Infinite words automata, semigroups, logic and games Dominique Perrin and Jean-Eric Pin
title_fullStr	Infinite words automata, semigroups, logic and games Dominique Perrin and Jean-Eric Pin
title_full_unstemmed	Infinite words automata, semigroups, logic and games Dominique Perrin and Jean-Eric Pin
title_short	Infinite words
title_sort	infinite words automata semigroups logic and games
title_sub	automata, semigroups, logic and games
topic	Automatentheorie - Halbgruppe - Mathematische Logik - Spieltheorie Gruppentheorie (DE-588)4072157-7 gnd Automatentheorie (DE-588)4003953-5 gnd
topic_facet	Automatentheorie - Halbgruppe - Mathematische Logik - Spieltheorie Gruppentheorie Automatentheorie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010744405&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV010177228
work_keys_str_mv	AT perrindominique infinitewordsautomatasemigroupslogicandgames AT pinjeaneric infinitewordsautomatasemigroupslogicandgames

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