Automata, Logics, and Infinite Games

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.

?-Automata.- Infinite Games.- Determinization and Complementation.- Determinization of Büchi-Automata.- Complementation of Büchi Automata Using Alternation.- Determinization and Complementation of Streett Automata.- Parity Games.- Memoryless Determinacy of Parity Games.- Algorithms for Parity Games.- Tree Automata.- Nondeterministic Tree Automata.- Alternating Tree Automata and Parity Games.- Modal ?-Calculus.- Modal ?-Calculus and Alternating Tree Automata.- Strictness of the Modal ?-Calculus Hierarchy.- Monadic Second-Order Logic.- Decidability of S1S and S2S.- The Complexity of Translating Logic to Finite Automata.- Expressive Power of Monadic Second-Order Logic and Modal ?-Calculus.- Tree-like Models.- Prefix-Recognizable Graphs and Monadic Logic.- The Monadic Theory of Tree-like Structures.- Two-Way Tree Automata Solving Pushdown Games.- Guarded Logics.- to Guarded Logics.- Automata for Guarded Fixed Point Logics.- Appendices.- Some Fixed Point Basics.