Cost-Parity and Cost-Streett Games
Résumé
We consider 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 omega-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 and co-NP. For cost-Streett games 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.
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