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Infinite words[electronic resource] :automata, semigroups, logic and games /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	512.2
書名/作者:	Infinite words : automata, semigroups, logic and games // Dominique Perrin and Jean-�Eric Pin.
作者:	Perrin, Dominique.
其他作者:	Pin, Jean Eric.
出版者:	Amsterdam ; : Elsevier,, 2004.
面頁冊數:	1 online resource (xi, 538 p.) : : ill.
附註:	"Academic Press."
標題:	Machine theory.
標題:	Group theory.
標題:	Automates math�ematiques, Th�eorie des.
標題:	Groupes, Th�eorie des.
標題:	Automatentheorie.
標題:	Speltheorie.
標題:	Logica.
標題:	Groepentheorie.
標題:	Topologie.
標題:	MATHEMATICS - Group Theory.
ISBN:	9780125321112
ISBN:	0125321112
ISBN:	9780080525648 (electronic bk.)
ISBN:	0080525644 (electronic bk.)
ISBN:	9786611025182
ISBN:	6611025189
書目註:	Includes bibliographical references (p. [499]-521).
內容註:	Cover -- Contents -- Preface -- Chapter I. AUTOMATA AND INFINITE WORDS -- 1. Introduction -- 2. Words and trees -- 3. Rational sets of infinite words -- 4. Automata -- 5. B�uchi automata -- 6. Deterministic B�uchi automata -- 7. Muller and Rabin automata -- 8. Transition automata -- 9. McNaughton's theorem -- 10. Computational complexity issues -- 11. Exercises -- 12. Notes -- Chapter II. AUTOMATA AND SEMIGROUPS -- 1. Introduction -- 2. Ramseyan factorizations and linked pairs -- 3. Recognition by morphism -- 4. Semigroups and infinite products -- 5. Wilke Algebras -- 6. Recognition by morphism of?-semigroups -- 7. The two modes of recognition -- 8. Syntactic congruence -- 9. Back to McNaughton's theorem -- 10. Prophetic automata -- 11. Exercises -- 12. Notes -- Chapter III. AUTOMATA AND TOPOLOGY -- 1. Introduction -- 2. Topological spaces -- 3. The space of infinite words -- 4. The space of finite or infinite words -- 5. Borel automata -- 6. Suslin sets -- 7. The separation theorem -- 8. Exercises -- 9. Notes -- Chapter IV. GAMES AND STRATEGIES -- 1. Introduction -- 2. Infinite games -- 3. Borel games -- 4. Games on graphs -- 5. Wadge games -- 6. Exercises -- 7. Notes -- Chapter V. WAGNER HIERARCHY -- 1. Introduction -- 2. Ordinals -- 3. Classes of sets -- 4. Chains -- 5. Superchains -- 6. The Wagner hierarchy -- 7. Exercises -- 8. Notes -- Chapter VI. VARIETIES -- 1. Introduction -- 2. Varieties of finite or infinite words -- 3. Varieties and topology -- 4. Weak recognition -- 5. Extensions of McNaughton's theorem -- 6. Varieties closed under aperiodic extension -- 7. Concatenation hierarchies for infinite words -- 8. Exercises -- 9. Notes -- Chapter VII. LOCAL PROPERTIES -- 1. Introduction -- 2. Weak recognition -- 3. Local properties of infinite words -- 4. Exercises -- 5. Notes -- Chapter VIII. AN EXCURSION INTO LOGIC -- 1. Introduction -- 2. The formalism of logic -- 3. Monadic second-order logic on words -- 4. First-order logic of the linear order -- 5. First-order logic of the successor -- 6. Temporal logic -- 7. Restricted temporal logic -- 8. Exercises -- 9. Notes -- Chapter IX. BI-INFINITE WORDS -- 1. Introduction -- 2. Bi-infinite words -- 3. Determinism -- 4. Morphisms -- 5. Unambiguous automata on bi-infinite words -- 6. Discrimination -- 7. Logic on Z -- 8. Exercises -- 9. Notes -- Chapter X. INFINITE TREES -- 1. Introduction -- 2. Finite and Infinite trees -- 3. Tree automata -- 4. Tree automata and games -- 5. Topology -- 6. Monadic second order logic of two successors -- 7. Effective algorithms -- 8. Exercises -- 9. Notes -- ANNEX A. FINITE SEMIGROUPS -- 1. Monoids.
摘要、提要註:	Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic. Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Bochi, McNaughton and Sch�atzenberger. Serves as both an introduction to the field and as a reference book. Contains numerous exercises desgined to aid students and readers. Self-contained chapters provide helpful guidance for lectures.
電子資源:	http://www.sciencedirect.com/science/book/9780125321112
電子資源:	Full text

Infinite words[electronic resource] :automata, semigroups, logic and games /
Perrin, Dominique.

Infinite wordsautomata, semigroups, logic and games /[electronic resource] :Dominique Perrin and Jean-�Eric Pin. - 1st ed. - Amsterdam ;Elsevier,2004. - 1 online resource (xi, 538 p.) :ill. - Pure and applied mathematics series ;141. - Pure and applied mathematics (Academic Press) ;142..

"Academic Press."

Includes bibliographical references (p. [499]-521).

Cover -- Contents -- Preface -- Chapter I. AUTOMATA AND INFINITE WORDS -- 1. Introduction -- 2. Words and trees -- 3. Rational sets of infinite words -- 4. Automata -- 5. B�uchi automata -- 6. Deterministic B�uchi automata -- 7. Muller and Rabin automata -- 8. Transition automata -- 9. McNaughton's theorem -- 10. Computational complexity issues -- 11. Exercises -- 12. Notes -- Chapter II. AUTOMATA AND SEMIGROUPS -- 1. Introduction -- 2. Ramseyan factorizations and linked pairs -- 3. Recognition by morphism -- 4. Semigroups and infinite products -- 5. Wilke Algebras -- 6. Recognition by morphism of?-semigroups -- 7. The two modes of recognition -- 8. Syntactic congruence -- 9. Back to McNaughton's theorem -- 10. Prophetic automata -- 11. Exercises -- 12. Notes -- Chapter III. AUTOMATA AND TOPOLOGY -- 1. Introduction -- 2. Topological spaces -- 3. The space of infinite words -- 4. The space of finite or infinite words -- 5. Borel automata -- 6. Suslin sets -- 7. The separation theorem -- 8. Exercises -- 9. Notes -- Chapter IV. GAMES AND STRATEGIES -- 1. Introduction -- 2. Infinite games -- 3. Borel games -- 4. Games on graphs -- 5. Wadge games -- 6. Exercises -- 7. Notes -- Chapter V. WAGNER HIERARCHY -- 1. Introduction -- 2. Ordinals -- 3. Classes of sets -- 4. Chains -- 5. Superchains -- 6. The Wagner hierarchy -- 7. Exercises -- 8. Notes -- Chapter VI. VARIETIES -- 1. Introduction -- 2. Varieties of finite or infinite words -- 3. Varieties and topology -- 4. Weak recognition -- 5. Extensions of McNaughton's theorem -- 6. Varieties closed under aperiodic extension -- 7. Concatenation hierarchies for infinite words -- 8. Exercises -- 9. Notes -- Chapter VII. LOCAL PROPERTIES -- 1. Introduction -- 2. Weak recognition -- 3. Local properties of infinite words -- 4. Exercises -- 5. Notes -- Chapter VIII. AN EXCURSION INTO LOGIC -- 1. Introduction -- 2. The formalism of logic -- 3. Monadic second-order logic on words -- 4. First-order logic of the linear order -- 5. First-order logic of the successor -- 6. Temporal logic -- 7. Restricted temporal logic -- 8. Exercises -- 9. Notes -- Chapter IX. BI-INFINITE WORDS -- 1. Introduction -- 2. Bi-infinite words -- 3. Determinism -- 4. Morphisms -- 5. Unambiguous automata on bi-infinite words -- 6. Discrimination -- 7. Logic on Z -- 8. Exercises -- 9. Notes -- Chapter X. INFINITE TREES -- 1. Introduction -- 2. Finite and Infinite trees -- 3. Tree automata -- 4. Tree automata and games -- 5. Topology -- 6. Monadic second order logic of two successors -- 7. Effective algorithms -- 8. Exercises -- 9. Notes -- ANNEX A. FINITE SEMIGROUPS -- 1. Monoids.

Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic. Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Bochi, McNaughton and Sch�atzenberger. Serves as both an introduction to the field and as a reference book. Contains numerous exercises desgined to aid students and readers. Self-contained chapters provide helpful guidance for lectures.

ISBN: 9780125321112

Source: 98488:98491Elsevier Science & Technologyhttp://www.sciencedirect.com

Nat. Bib. Agency Control No.: 0125321112UkSubjects--Topical Terms:

173754
Machine theory.
Index Terms--Genre/Form:

336502
Electronic books.

LC Class. No.: QA267 / .P47 2004eb

Dewey Class. No.: 512.2

Infinite words[electronic resource] :automata, semigroups, logic and games /
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