Cost-Parity and Cost-Streett Games

Nathanael Fijalkow, Martin Zimmermann, Marc Herbstritt
2012 Foundations of Software Technology and Theoretical Computer Science  
We consider two-player games played on graphs equipped with costs on edges and introduce two winning conditions, cost-parity and cost-Streett, which require bounds on the cost between requests and their responses. Both conditions generalize the corresponding classical ω-regular conditions as well as the corresponding finitary conditions. For cost-parity games we show that the first player has positional winning strategies and that determining the winner lies in NP ∩ coNP. For cost-Streett games
more » ... we show that the first player has finite-state winning strategies and that determining the winner is EXPTIME-complete. This unifies the complexity results for the classical and finitary variants of these games. Both types of cost-games can be solved by solving linearly many instances of their classical variants.
doi:10.4230/lipics.fsttcs.2012.124 dblp:conf/fsttcs/FijalkowZ12 fatcat:4nnmkdmxhzdo7cpwfsralntzey