Abstract
This paper proposes a new algorithm that improves the complexity bound for solving parity games. Our approach combines McNaughton’s iterated fixed point algorithm with a preprocessing step, which is called prior to every recursive call. The preprocessing uses ranking functions similar to Jurdziński’s, but with a restricted codomain, to determine all winning regions smaller than a predefined parameter. The combination of the preprocessing step with the recursive call guarantees that McNaughton’s algorithm proceeds in big steps, whose size is bounded from below by the chosen parameter. Higher parameters result in smaller call trees, but to the cost of an expensive preprocessing step. An optimal parameter balances the cost of the recursive call and the preprocessing step, resulting in an improvement of the known upper bound for solving parity games from approximately \(O(m\,n^{\frac{1}{2}c})\) to \( O(m\,n^{\frac{1}{3}c})\).KeywordsModel CheckRanking FunctionHigh ColorRecursive CallWinning StrategyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.