## Automata, Logics, and Infinite Games: A Guide to Current ResearchA 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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### Contents

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 |

377 | |

381 | |

### Other editions - View all

Automata, Logics, and Infinite Games: A Guide to Current Research Erich Gr?del,Wolfgang Thomas,Thomas Wilke No preview available - 2002 |

Automata, Logics, and Infinite Games: A Guide to Current Research Erich Grädel,Wolfgang Thomas,Thomas Wilke No preview available - 2002 |