Automata, Logics, and Infinite Games: A Guide to Current Research

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Erich Grädel, Wolfgang Thomas, Thomas Wilke
Springer, 02.08.2003 - 392 Seiten

A central aim and ever-lasting dream of computer science is to put the development of hardware and software systems on a mathematical basis which is both firm and practical. Such a scientific foundation is needed especially for the construction of reactive programs, like communication protocols or control systems.

For the construction and analysis of reactive systems an elegant and powerful theory has been developed based on automata theory, logical systems for the specification of nonterminating behavior, and infinite two-person games.

The 19 chapters presented in this multi-author monograph give a consolidated overview of the research results achieved in the theory of automata, logics, and infinite games during the past 10 years. Special emphasis is placed on coherent style, complete coverage of all relevant topics, motivation, examples, justification of constructions, and exercises.

 

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Inhalt

Introduction
2
ωAutomata
3
Infinite Games
22
Notes on Part I
39
Determinization and Complementation
41
Determinization of BuchiAutomata
43
Complementation of Büchi Automata Using Alternation
61
Determinization and Complementation of Streett Automata
79
Monadic SecondOrder Logic
204
Decidability of S1S and S2S
207
The Complexity of Translating Logic to Finite Automata
231
Expressive Power of Monadic SecondOrder Logic and Modal µCalculus
239
Notes on Part VI
258
Treelike Models
260
PrefixRecognizable Graphs and Monadic Logic
263
The Monadic Theory of Treelike Structures
284

Notes on Part II
92
Parity Games
93
Memoryless Determinacy of Parity Games
94
Algorithms for Parity Games
107
Notes on Part III
130
Tree Automata
132
Nondeterministic Tree Automata
133
Alternating Tree Automata and Parity Games
153
Notes on Part IV
168
Modal µCalculus
169
Modal µCalculus and Alternating Tree Automata
176
Strictness of the Modal µCalculus Hierarchy
185
Notes on Part V
202
TwoWay Tree Automata Solving Pushdown Games
303
Notes on Part VII
318
Guarded Logics
319
Introduction to Guarded Logics
320
Automata for Guarded Fixed Point Logics
343
Notes on Part VIII
356
Appendices
357
Some Fixed Point Basics
358
Literature
365
Symbol Index
377
Index
381
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