Cost-Parity and Cost-Streett Games

Nathanaël Fijalkow (1, 2) , Martin Zimmermann (2)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]

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.

Mots clés: Parity Games; Streett Games; Costs; Scoring Functions

Domaines: Informatique et théorie des jeux [cs.GT]

Nathanaël Fijalkow, Martin Zimmermann. Cost-Parity and Cost-Streett Games. 2012. ⟨hal-00714012v1⟩