The complexity of mean-payoff pushdown games Journal Article


Author(s): Chatterjee, Krishnendu; Velner, Yaron
Article Title: The complexity of mean-payoff pushdown games
Affiliation IST Austria
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 model the control flow of sequential programs with recursion.While pushdown games have been studied before with qualitative objectives-such as reachability and ?-regular objectives- in this work, we study for the first time such games with the most well-studied quantitative objective, the mean-payoff objective. In pushdown games, two types of strategies are relevant: (1) global strategies, which depend on the entire global history; and (2) modular strategies, which have only local memory and thus do not depend on the context of invocation but rather 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 by 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 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.
Keywords: mean-payoff objectives; Graph games; Pushdown systems; Quantitative verification and synthesis
Journal Title: Journal of the ACM
Volume: 64
Issue 5
ISSN: 0004-5411
Publisher: ACM  
Date Published: 2017-09-01
Start Page: Article number: 34
DOI: 10.1145/3121408
Notes: The research was partially supported by Austrian Science Fund (FWF) Grant No. P 23499-N23, FWF NFN Grant No. S11407-N23 (RiSE/SHiNE), ERC Start grant (279307: Graph Games), Microsoft faculty fellows award, the Israeli Centers of Research Excellence (I-CORE) program, (Center No. 4/11), and the RICH Model Toolkit (ICT COST Action IC0901).
Open access: no
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