Alternating traps in Muller and parity games

A. Grinshpun, P. Phalitnonkiat, S. Rubin, A. Tarfulea, Theoretical Computer Science 521 (2014) 73–91.


Journal Article | Published | English
Author
; ; ;
Department
Abstract
Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different classes and representations of Muller games lead to problems of varying computational complexity. One such class are parity games; these are of particular significance in computational complexity, as they remain one of the few combinatorial problems known to be in NP ∩ co-NP but not known to be in P. We show that winning regions for a Muller game can be determined from the alternating structure of its traps. To every Muller game we then associate a natural number that we call its trap depth; this parameter measures how complicated the trap structure is. We present algorithms for parity games that run in polynomial time for graphs of bounded trap depth, and in general run in time exponential in the trap depth.
Publishing Year
Date Published
2014-02-13
Journal Title
Theoretical Computer Science
Volume
521
Page
73 - 91
ISSN
IST-REx-ID

Cite this

Grinshpun A, Phalitnonkiat P, Rubin S, Tarfulea A. Alternating traps in Muller and parity games. Theoretical Computer Science. 2014;521:73-91. doi:10.1016/j.tcs.2013.11.032
Grinshpun, A., Phalitnonkiat, P., Rubin, S., & Tarfulea, A. (2014). Alternating traps in Muller and parity games. Theoretical Computer Science, 521, 73–91. https://doi.org/10.1016/j.tcs.2013.11.032
Grinshpun, Andrey, Pakawat Phalitnonkiat, Sasha Rubin, and Andrei Tarfulea. “Alternating Traps in Muller and Parity Games.” Theoretical Computer Science 521 (2014): 73–91. https://doi.org/10.1016/j.tcs.2013.11.032.
A. Grinshpun, P. Phalitnonkiat, S. Rubin, and A. Tarfulea, “Alternating traps in Muller and parity games,” Theoretical Computer Science, vol. 521, pp. 73–91, 2014.
Grinshpun A, Phalitnonkiat P, Rubin S, Tarfulea A. 2014. Alternating traps in Muller and parity games. Theoretical Computer Science. 521, 73–91.
Grinshpun, Andrey, et al. “Alternating Traps in Muller and Parity Games.” Theoretical Computer Science, vol. 521, Elsevier, 2014, pp. 73–91, doi:10.1016/j.tcs.2013.11.032.

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar