Memory Reduction for Strategies in Infinite Games
نویسندگان
چکیده
In this thesis we deal with the problem of reducing the memory necessary for implementing winning strategies in infinite games. We present an algorithm that is based on the notion of game reduction. Its key idea is to reduce the problem of computing a solution to a given game to computing a solution to a new game. This new game has an extended game graph which contains the memory to solve the original game. Our algorithm computes an equivalence relation on the vertices of the extended game graph and from that deduces equivalent memory contents. The computations are carried out via a transformation to ω-automata. We apply our algorithm to Request-Response and Staiger-Wagner games where in both cases we obtain a running time exponential in the size of the given game graph. We compare our method to another technique of memory reduction, namely the minimisation algorithm for finite automata with output. For each of the two approaches we present an example for which it yields a substantially better result than the other approach.
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