Uniform Solution of Parity Games on Prefix-Recognizable Graphs

Cachat, Thierry

doi:10.1016/s1571-0661(04)80534-6

Cited by 30 publications

(26 citation statements)

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“…We prove that already the reachability problem on prefix-recognizable graphs is EXP-hard. Since solving parity games on prefix-recognizable is in EXP [3], it immediately follows that alternating reachability is in EXP too. Thus surprisingly, both reachability 0020-0190/$ -see front matter © 2008 Elsevier B.V. All rights reserved.…”

Section: Introductionmentioning

confidence: 99%

Reachability on prefix-recognizable graphs

Göller

2008

Information Processing Letters

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Section: Introductionmentioning

confidence: 99%

Reachability on prefix-recognizable graphs

Göller

2008

Information Processing Letters

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“…This includes e.g. decidability of monadic second order logic [9] and the existence of uniform winning strategies for parity games [6]. The decidability questions for bisimilarity are, however, more intricate.…”

Section: Introductionmentioning

confidence: 99%

Undecidability Results for Bisimilarity on Prefix Rewrite Systems

Jancar¹,

Srba²

2006

BRICS

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Abstract.We answer an open question related to bisimilarity checking on labelled transition systems generated by prefix rewrite rules on words. Stirling (1996Stirling ( , 1998 proved the decidability of bisimilarity for normed pushdown processes. This result was substantially extended by Sénizergues (1998Sénizergues ( , 2005 who showed the decidability for regular (or equational) graphs of finite out-degree (which include unnormed pushdown processes). The question of decidability of bisimilarity for a more general class of so called Type -1 systems (generated by prefix rewrite rules of the form R a −→ w where R is a regular language) was left open; this was repeatedly indicated by both Stirling and Sénizergues. Here we answer the question negatively, i.e., we show undecidability of bisimilarity on Type -1 systems, even in the normed case. We complete the picture by considering classes of systems that use rewrite rules of the form w a −→ R and R1 a −→ R2 and show when they yield low undecidability (Π 0 1 -completeness) and when high undecidability (Σ 1 1 -completeness), all with and without the assumption of normedness.

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“…More precisely, he proposed an effective construction of an alternating automaton recognizing precisely the winning configurations. Cachat also states in [1] that the set of winning positions for parity games is regular. The proof of [1] is only sketched and the cmoplexity of the computation is not clear.…”

Section: Introductionmentioning

confidence: 99%

“…Cachat also states in [1] that the set of winning positions for parity games is regular. The proof of [1] is only sketched and the cmoplexity of the computation is not clear. Note that the results of this paper were found independently of [1].…”

Section: Introductionmentioning

confidence: 99%

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Note on winning positions on pushdown games with ω-regular conditions

Serre¹

2003

Information Processing Letters

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We consider infinite two-player games on pushdown graphs. For parity winning conditions, we show that the set of winning positions of each player is regular and we give an effective construction of an alternating automaton recognizing it. This provides a DEXPTIME procedure to decide whether a position is winning for a given player. Finally, using the same methods, we show, for any ω-regular winning condition, that the set of winning positions for a given player is regular and effective.

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Uniform Solution of Parity Games on Prefix-Recognizable Graphs

Cited by 30 publications

References 1 publication

Reachability on prefix-recognizable graphs

Reachability on prefix-recognizable graphs

Undecidability Results for Bisimilarity on Prefix Rewrite Systems

Note on winning positions on pushdown games with ω-regular conditions

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