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Cost-Parity and Cost-Streett Games

Authors Nathanael Fijalkow, Martin Zimmermann



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Nathanael Fijalkow
Martin Zimmermann

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Nathanael Fijalkow and Martin Zimmermann. Cost-Parity and Cost-Streett Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 18, pp. 124-135, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.FSTTCS.2012.124

Abstract

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 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 intersection 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.
Keywords
  • Parity Games
  • Streett Games
  • Costs
  • Scoring Functions

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