## Paper: Mean-Payoff Parity Games (at LICS 2005)

**Krishnendu Chatterjee Thomas A. Henzinger Marcin Jurdzinski**

### Abstract

Games played on graphs may have qualitative objectives, such as the satisfaction of an ?-regular property, or quantitative objectives, such as the optimization of a realvalued reward. When games are used to model reactive systems with both fairness assumptions and quantitative (e.g., resource) constraints, then the corresponding objective combines both a qualitative and a quantitative component. In a general case of interest, the qualitative component is a parity condition and the quantitative component is a mean-payoff reward. We study and solve such mean-payoff parity games. We also prove some interesting facts about mean-payoff parity games which distinguish them both from mean-payoff and from parity games. In particular, we show that optimal strategies exist in mean-payoff parity games, but they may require infinite memory.

### BibTeX

@InProceedings{ChatterjeeHenzinger-MeanPayoffParityGam, author = {Krishnendu Chatterjee and Thomas A. Henzinger and Marcin Jurdzinski}, title = {Mean-Payoff Parity Games}, booktitle = {Proceedings of the Twentieth Annual IEEE Symposium on Logic in Computer Science (LICS 2005)}, year = {2005}, month = {June}, pages = {178--187}, location = {Chicago, USA}, publisher = {IEEE Computer Society Press} }