Abstract
We study infinite two-player games over pushdown graphs with a winning condition that refers explicitly to the infinity of the game graph: A play is won by player 0 if some vertex is visited infinity often during the play. We show that the set of winning plays is a proper ∑3-set in the Borel hierarchy, thus transcending the Boolean closure of ∑2-sets which arises with the standard automata theoretic winning conditions (such as the Muller, Rabin, or parity condition). We also show that this ∑3-game over pushdown graphs can be solved effectively (by a computation of the winning region of player 0 and his memoryless winning strategy). This seems to be a first example of an effectively solvable game beyond the second level of the Borel hierarchy.
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Cachat, T., Duparc, J., Thomas, W. (2002). Solving Pushdown Games with a ∑3 Winning Condition. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_22
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DOI: https://doi.org/10.1007/3-540-45793-3_22
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