An ordered approach to solving parity games in quasi-polynomial time and quasi-linear space

• Published in: International journal on software tools for technology transfer Vol. 21; no. 3; pp. 325 - 349
• Main Authors: Fearnley, John, Jain, Sanjay, de Keijzer, Bart, Schewe, Sven, Stephan, Frank, Wojtczak, Dominik
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-06-2019; Springer Nature B.V
• Subjects: Algorithms; Color matching; Complexity; Computer Science; Data structures; Games; Lower bounds; Parity; Polynomials; Production scheduling; Software Engineering; Software Engineering/Programming and Operating Systems; Spin 2017; Theory of Computation; Parity games; Quasi-polynomial; Progress measure
• ISSN: 1433-2779; 1433-2787
• DOI: 10.1007/s10009-019-00509-3

Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have recently shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their data structure as a progress measure, allowing for a backward implementation instead of a complete unravelling of the game. To achieve this, a number of changes have to be made to their techniques, where the main one is to add power to the antagonistic player that allows for determining her rational move without changing the outcome of the game. We provide a first implementation for a quasi-polynomial algorithm, test it on small examples, and provide a number of side results, including minor algorithmic improvements, a quasi-bi-linear complexity in the number of states and edges for a fixed number of colours, matching lower bounds for the algorithm of Calude et al., and a complexity index associated to our approach, which we compare to the recently proposed register index.