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Qualitative concurrent parity games

K. Chatterjee, L. De Alfaro, T.A. Henzinger, ACM Transactions on Computational Logic (TOCL) 12 (2011).

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Journal Article | Published | English
Abstract
We consider two-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. We consider ω-regular winning conditions specified as parity objectives. Both players are allowed to use randomization when choosing their moves. We study the computation of the limit-winning set of states, consisting of the states where the sup-inf value of the game for player 1 is 1: in other words, a state is limit-winning if player 1 can ensure a probability of winning arbitrarily close to 1. We show that the limit-winning set can be computed in O(n2d+2) time, where n is the size of the game structure and 2d is the number of priorities (or colors). The membership problem of whether a state belongs to the limit-winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms are considerably more involved than those for turn-based games. This is because concurrent games do not satisfy two of the most fundamental properties of turn-based parity games. First, in concurrent games limit-winning strategies require randomization; and second, they require infinite memory.
Publishing Year
Date Published
2011-07-04
Journal Title
ACM Transactions on Computational Logic (TOCL)
Volume
12
Issue
4
Article Number
28
IST-REx-ID

Cite this

Chatterjee K, De Alfaro L, Henzinger TA. Qualitative concurrent parity games. ACM Transactions on Computational Logic (TOCL). 2011;12(4). doi:10.1145/1970398.1970404
Chatterjee, K., De Alfaro, L., & Henzinger, T. A. (2011). Qualitative concurrent parity games. ACM Transactions on Computational Logic (TOCL), 12(4). https://doi.org/10.1145/1970398.1970404
Chatterjee, Krishnendu, Luca De Alfaro, and Thomas A Henzinger. “Qualitative Concurrent Parity Games.” ACM Transactions on Computational Logic (TOCL) 12, no. 4 (2011). https://doi.org/10.1145/1970398.1970404.
K. Chatterjee, L. De Alfaro, and T. A. Henzinger, “Qualitative concurrent parity games,” ACM Transactions on Computational Logic (TOCL), vol. 12, no. 4, 2011.
Chatterjee K, De Alfaro L, Henzinger TA. 2011. Qualitative concurrent parity games. ACM Transactions on Computational Logic (TOCL). 12(4).
Chatterjee, Krishnendu, et al. “Qualitative Concurrent Parity Games.” ACM Transactions on Computational Logic (TOCL), vol. 12, no. 4, 28, ACM, 2011, doi:10.1145/1970398.1970404.

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