Please use this identifier to cite or link to this item: https://doi.org/10.1007/s10009-019-00509-3
Title: An ordered approach to solving parity games in quasi-polynomial time and quasi-linear space
Authors: Fearnley J.
Jain S. 
de Keijzer B.
Schewe S.
Stephan F. 
Wojtczak D.
Keywords: Parity games
Progress measure
Quasi-polynomial
Issue Date: 2019
Publisher: Springer Verlag
Citation: Fearnley J., Jain S., de Keijzer B., Schewe S., Stephan F., Wojtczak D. (2019). An ordered approach to solving parity games in quasi-polynomial time and quasi-linear space. International Journal on Software Tools for Technology Transfer 21 (3) : 325-349. ScholarBank@NUS Repository. https://doi.org/10.1007/s10009-019-00509-3
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, 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. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
Source Title: International Journal on Software Tools for Technology Transfer
URI: https://scholarbank.nus.edu.sg/handle/10635/177521
ISSN: 1433-2779
DOI: 10.1007/s10009-019-00509-3
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