Mean payoff pushdown games

K. Chatterjee, Y. Velner, in:, Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, IEEE, 2012, p. 6280438.

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Abstract
Two-player games on graphs are central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can model the control flow of sequential programs with recursion. While pushdown games have been studied before with qualitative objectives, such as reachability and parity objectives, in this work we study for the first time such games with the most well-studied quantitative objective, namely, mean payoff objectives. In pushdown games two types of strategies are relevant: (1) global strategies, that depend on the entire global history; and (2) modular strategies, that have only local memory and thus do not depend on the context of invocation, but only on the history of the current invocation of the module. Our main results are as follows: (1) One-player pushdown games with mean-payoff objectives under global strategies are decidable in polynomial time. (2) Two-player pushdown games with mean-payoff objectives under global strategies are undecidable. (3) One-player pushdown games with mean-payoff objectives under modular strategies are NP-hard. (4) Two-player pushdown games with mean-payoff objectives under modular strategies can be solved in NP (i.e., both one-player and two-player pushdown games with mean-payoff objectives under modular strategies are NP-complete). We also establish the optimal strategy complexity showing that global strategies for mean-payoff objectives require infinite memory even in one-player pushdown games; and memoryless modular strategies are sufficient in two-player pushdown games. Finally we also show that all the problems have the same computational complexity if the stack boundedness condition is added, where along with the mean-payoff objective the player must also ensure that the stack height is bounded.
Publishing Year
Date Published
2012-08-23
Proceedings Title
Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science
Acknowledgement
The research was supported by Austrian Science Fund (FWF) Grant No P 23499-N23, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), Microsoft faculty fellows award, the Israeli Centers of Research Excellence (ICORE) program, (Center No. 4/11), the RICH Model Toolkit (ICT COST Action IC0901), and was carried out in partial fulfillment of the requirements for the Ph.D. degree of the second author. A Technical Report of this paper is available via internal link.
Article Number
6280438
Conference
LICS: Logic in Computer Science
Conference Location
Dubrovnik, Croatia
Conference Date
2012-06-25 – 2012-06-28
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Chatterjee K, Velner Y. Mean payoff pushdown games. In: Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. IEEE; 2012:6280438. doi:10.1109/LICS.2012.30
Chatterjee, K., & Velner, Y. (2012). Mean payoff pushdown games. In Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science (p. 6280438). Dubrovnik, Croatia : IEEE. https://doi.org/10.1109/LICS.2012.30
Chatterjee, Krishnendu, and Yaron Velner. “Mean Payoff Pushdown Games.” In Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, 6280438. IEEE, 2012. https://doi.org/10.1109/LICS.2012.30.
K. Chatterjee and Y. Velner, “Mean payoff pushdown games,” in Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, Dubrovnik, Croatia , 2012, p. 6280438.
Chatterjee K, Velner Y. 2012. Mean payoff pushdown games. Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science. LICS: Logic in Computer Science 6280438.
Chatterjee, Krishnendu, and Yaron Velner. “Mean Payoff Pushdown Games.” Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science, IEEE, 2012, p. 6280438, doi:10.1109/LICS.2012.30.
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