Abstract
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. The key idea of a game reduction is to reduce the problem of computing a solution for a given game to the problem of computing a solution for a new game which has an extended game graph but a simpler winning condition. The new game graph 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. We apply our algorithm to Request-Response and Staiger-Wagner games where in both cases we obtain a running time polynomial in the size of the extended game graph. We compare our method to the technique of minimising strategy automata and present an example for which our approach yields a substantially better result.
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Holtmann, M., Löding, C. (2007). Memory Reduction for Strategies in Infinite Games. In: Holub, J., Žďárek, J. (eds) Implementation and Application of Automata. CIAA 2007. Lecture Notes in Computer Science, vol 4783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76336-9_24
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DOI: https://doi.org/10.1007/978-3-540-76336-9_24
Publisher Name: Springer, Berlin, Heidelberg
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