Bisimulation and Language Equivalence

Stirling, Colin

doi:10.1007/0-306-48088-3_7

Cited by 3 publications

(1 citation statement)

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“…We use the terminology introduced by Stirling (see, e.g., [30]). In the following table, R 1 , R 2 and R stand for regular sets over Γ ; w, w stand for elements of Γ * (the respective regular languages are thus singletons); and X, Y, p, q stand for elements of Γ .…”

Section: Propositionmentioning

confidence: 99%

Undecidability Results for Bisimilarity on Prefix Rewrite Systems

Jancar

Srba

2006

Lecture Notes in Computer Science

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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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Section: Propositionmentioning

confidence: 99%