Elsevier

Theoretical Computer Science

Volume 458, 2 November 2012, Pages 49-60
Theoretical Computer Science

Energy parity games

https://doi.org/10.1016/j.tcs.2012.07.038Get rights and content
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Abstract

Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own interest in the design and synthesis of resource-constrained omega-regular specifications, energy parity games provide one of the simplest model of games with combined qualitative and quantitative objectives. Our main results are as follows: (a) exponential memory is sufficient and may be necessary for winning strategies in energy parity games; (b) the problem of deciding the winner in energy parity games can be solved in NP  coNP; and (c) we give an algorithm to solve energy parity by reduction to energy games. We also show that the problem of deciding the winner in energy parity games is logspace-equivalent to the problem of deciding the winner in mean-payoff parity games, which can thus be solved in NP  coNP. As a consequence we also obtain a conceptually simple algorithm to solve mean-payoff parity games.

Keywords

Games on graphs
Parity objectives
Quantitative objectives

Cited by (0)

This is an improved version of a paper that appeared in the Proceedings of the 37th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science 6199, Springer-Verlag, 2010, pages 599–610. The present version contains detailed proofs, and improved memory and algorithmic complexity bounds. This work was partially supported by FWF Grant No P 23499-N23, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.