An Accelerated Algorithm for 3-Color Parity Games with an Application to Timed Games

摘要

Three-color parity games capture the disjunction of a Buechi and a co-Buechi condition. The most efficient known algorithm for these games is the progress measures algorithm by Jurdzinski. We present an acceleration technique that, while leaving the worst-case complexity unchanged, often leads to considerable speed-ups in games arising in practice. As an application, we consider games played in discrete real time, where players should be prevented from stopping time by always choosing moves with delay zero. The time progress condition can be encoded as a three-color parity game. Using the tool TICC as a platform, we compare the performance of a BDD-based symbolic implementation of the progress measure algorithm with acceleration, and of the symbolic implementation of the classical μ-calculus algorithm of Emerson and Jutla.