@MISC{Thomas95onthe, author = {Wolfgang Thomas}, title = {On the Synthesis of Strategies in Infinite Games}, year = {1995} }

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Abstract

. Infinite two-person games are a natural framework for the study of reactive nonterminating programs. The effective construction of winning strategies in such games is an approach to the synthesis of reactive programs. We describe the automata theoretic setting of infinite games (given by "game graphs"), outline a new construction of winning strategies in finite-state games, and formulate some questions which arise for games over effectively presented infinite graphs. 1 Introduction One of the origins of automata theory over infinite strings was the interest in verifying and synthesizing switching circuits. These circuits were considered as transforming infinite input sequences into output sequences, and systems of restricted arithmetic served as specification formalisms ([Ch63]). With Buchi's decision procedure for the monadic second-order theory S1S of one successor ([Bu62]), it turned out that the "solution problem" (in more recent terminology: the verification problem or model ch...