Authors: Nathanaël Fijalkow ; Martin Zimmermann

We consider two-player games played on finite 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 and the corresponding finitary conditions. For parity games with costs we show that the first player has positional winning strategies and that determining the winner lies in NP and coNP. For Streett games with costs we show that the first player has finite-state winning strategies and that determining the winner is EXPTIME-complete. The second player might need infinite memory in both games.
Both types of games with costs can be solved by solving linearly many instances of their classical variants.

Comment: A preliminary version of this work appeared in FSTTCS 2012 under the name "Cost-parity and Cost-Streett Games". The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreements 259454 (GALE) and 239850 (SOSNA)

• 03D05 - Automata and formal grammars in connection with logical questions
• 68Q25 - Analysis of algorithms and problem complexity
• 68Q45 - Formal languages and automata
• 68Q60 - Specification and verification (program logics, model checking, etc.)
• 91A05 - 2-person games
• 91A43 - Games involving graphs