Strategy construction in infinite games with streett and rabin chain winning conditions

Abstract

We consider finite-state games as a model of nonterminating reactive computations. A natural type of specification is given by games with Streett winning condition (corresponding to automata accepting by conjunctions of fairness conditions). We present an algorithm which solves the problem of program synthesis for these specifications. We proceed in two steps: First, we give a reduction of Streett automata to automata with the Rabin chain (or parity) acceptance condition. Secondly, we develop an inductive strategy construction over Rabin chain automata which yields finite automata that realize winning strategies. For the step from Rabin chain games to winning strategies examples are discussed, based on an implementation of the algorithm.