Jurdziński, Marcin ; Kupferman, Orna ; Henzinger, Thomas AIST Austria
Behavioral properties of open systems can be formalized as objectives in two-player games. Turn-based games model asynchronous interaction between the players (the system and its environment) by interleaving their moves. Concurrent games model synchronous interaction: the players always move simultaneously. Infinitary winning criteria are considered: Büchi, co-Büchi, and more general parity conditions. A generalization of determinacy for parity games to concurrent parity games demands probabilistic (mixed) strategies: either player 1 has a mixed strategy to win with probability 1 (almost-sure winning), or player 2 has a mixed strategy to win with positive probability. This work provides efficient reductions of concurrent probabilistic Büchi and co-Büchi games to turn-based games with Büchi condition and parity winning condition with three priorities, respectively. From a theoretical point of view, the latter reduction shows that one can trade the probabilistic nature of almost-sure winning for a more general parity (fairness) condition. The reductions improve understanding of concurrent games and provide an alternative simple proof of determinacy of concurrent Büchi and co-Büchi games. From a practical point of view, the reductions turn solvers of turn-based games into solvers of concurrent probabilistic games. Thus improvements in the well-studied algorithms for the former carry over immediately to the latter. In particular, a recent improvement in the complexity of solving turn-based parity games yields an improvement in time complexity of solving concurrent probabilistic co-Büchi games from cubic to quadratic.
This research was supported in part by the Polish KBN grant 7-T11C-027-20, the AFOSR MURI grant F49620-00-1-0327, and the NSF Theory grant CCR-9988172.
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CSL: Computer Science Logic
Jurdziński M, Kupferman O, Henzinger TA. Trading probability for fairness. In: Vol 2471. Springer; 2002:292-305. doi:10.1007/3-540-45793-3_20
Jurdziński, M., Kupferman, O., & Henzinger, T. A. (2002). Trading probability for fairness (Vol. 2471, pp. 292–305). Presented at the CSL: Computer Science Logic, Springer. https://doi.org/10.1007/3-540-45793-3_20
Jurdziński, Marcin, Orna Kupferman, and Thomas A Henzinger. “Trading Probability for Fairness,” 2471:292–305. Springer, 2002. https://doi.org/10.1007/3-540-45793-3_20.
M. Jurdziński, O. Kupferman, and T. A. Henzinger, “Trading probability for fairness,” presented at the CSL: Computer Science Logic, 2002, vol. 2471, pp. 292–305.
Jurdziński M, Kupferman O, Henzinger TA. 2002. Trading probability for fairness. CSL: Computer Science Logic, LNCS, vol. 2471. 292–305.
Jurdziński, Marcin, et al. Trading Probability for Fairness. Vol. 2471, Springer, 2002, pp. 292–305, doi:10.1007/3-540-45793-3_20.