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Computer Science > Computational Complexity

arXiv:1010.2420 (cs)
[Submitted on 12 Oct 2010 (v1), last revised 3 Feb 2012 (this version, v2)]

Title:The surprizing complexity of generalized reachability games

Authors:Nathanaël Fijalkow (LIAFA), Florian Horn (LIAFA)
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Abstract:Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such games is $\PSPACE$-complete, although it is fixed-parameter tractable with the number of reachability objectives as parameter. Moreover, we consider the memory requirements for both players and give matching upper and lower bounds on the size of winning strategies. In order to allow more efficient algorithms, we consider subclasses of generalized reachability games. We show that bounding the size of the reachability sets gives two natural subclasses where deciding the winner can be done efficiently.
Subjects: Computational Complexity (cs.CC); Computer Science and Game Theory (cs.GT); Logic in Computer Science (cs.LO)
Cite as: arXiv:1010.2420 [cs.CC]
  (or arXiv:1010.2420v2 [cs.CC] for this version)
  https://doi.org/10.48550/arXiv.1010.2420

Submission history

From: Nathanael Fijalkow [view email] [via CCSD proxy]
[v1] Tue, 12 Oct 2010 15:27:15 UTC (22 KB)
[v2] Fri, 3 Feb 2012 07:35:03 UTC (42 KB)
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