Chatterjee, KrishnenduIST Austria ; Doyen, Laurent ; Randour, Mickael ; Raskin, Jean
We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multi-dimensional mean-payoff games that are known to be coNP-complete, multi-dimensional total-payoff games are undecidable. We introduce conservative approximations of these objectives, where the payoff is considered over a local finite window sliding along a play, instead of the whole play. For single dimension, we show that (i) if the window size is polynomial, deciding the winner takes polynomial time, and (ii) the existence of a bounded window can be decided in NP ∩ coNP, and is at least as hard as solving mean-payoff games. For multiple dimensions, we show that (i) the problem with fixed window size is EXPTIME-complete, and (ii) there is no primitive-recursive algorithm to decide the existence of a bounded window.
279307; ERC; Fonds National de la Reserche Luxembourg; 279499; ERC; Fonds National de la Reserche Luxembourg
118 - 132
ATVA: Automated Technology for Verification and Analysis
2013-10-15 – 2013-10-18
Chatterjee K, Doyen L, Randour M, Raskin J. Looking at mean-payoff and total-payoff through windows. 2013;8172:118-132. doi:10.1007/978-3-319-02444-8_10
Chatterjee, K., Doyen, L., Randour, M., & Raskin, J. (2013). Looking at mean-payoff and total-payoff through windows. Presented at the ATVA: Automated Technology for Verification and Analysis, Hanoi, Vietnam: Springer. https://doi.org/10.1007/978-3-319-02444-8_10
Chatterjee, Krishnendu, Laurent Doyen, Mickael Randour, and Jean Raskin. “Looking at Mean-Payoff and Total-Payoff through Windows.” Lecture Notes in Computer Science. Springer, 2013. https://doi.org/10.1007/978-3-319-02444-8_10.
K. Chatterjee, L. Doyen, M. Randour, and J. Raskin, “Looking at mean-payoff and total-payoff through windows,” vol. 8172. Springer, pp. 118–132, 2013.
Chatterjee K, Doyen L, Randour M, Raskin J. 2013. Looking at mean-payoff and total-payoff through windows. 8172, 118–132.
Chatterjee, Krishnendu, et al. Looking at Mean-Payoff and Total-Payoff through Windows. Vol. 8172, Springer, 2013, pp. 118–32, doi:10.1007/978-3-319-02444-8_10.
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