An Ordered Approach to Solving Parity Games in Quasi Polynomial Time and Quasi Linear Space



Fearnley, John, Jain, Sanjay, Schewe, Sven ORCID: 0000-0002-9093-9518, Stephan, Frank and Wojtczak, Dominik ORCID: 0000-0001-5560-0546
(2017) An Ordered Approach to Solving Parity Games in Quasi Polynomial Time and Quasi Linear Space. In: ISSTA '17: International Symposium on Software Testing and Analysis.

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Abstract

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, and matching lower bounds for the algorithm of Calude et al.

Item Type: Conference or Workshop Item (Unspecified)
Uncontrolled Keywords: parity games, model checking games, synthesis
Depositing User: Symplectic Admin
Date Deposited: 24 May 2017 07:38
Last Modified: 09 May 2023 17:26
DOI: 10.1145/3092282.3092286
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3007624