Undecidability results for bisimilarity on prefix rewrite systems

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dc.contributor.author Jančar, Petr
dc.contributor.author Srba, Jiří
dc.date.accessioned 2006-09-25T09:08:14Z
dc.date.available 2006-09-25T09:08:14Z
dc.date.issued 2006
dc.identifier.citation Foundations of software science and computation structures : 9th International Conference, FOSSACS 2006, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2006, Vienna, Austria, March 25-31, 2006. Proceedings. 2006, p. 277-291. Lecture notes in computer science, vol. 3921. en
dc.identifier.isbn 978-3-540-33045-5
dc.identifier.issn 0302-9743
dc.identifier.uri http://hdl.handle.net/10084/56467
dc.language.iso en en
dc.publisher Springer en
dc.relation.ispartofseries Foundations of software science and computation structures en
dc.relation.uri http://dx.doi.org/10.1007/11690634_19 en
dc.subject pushdown-automata
dc.subject bisimulation
dc.subject equivalence
dc.subject decidability
dc.title Undecidability results for bisimilarity on prefix rewrite systems en
dc.type article en
dc.identifier.location Není ve fondu ÚK en
dc.description.abstract-en We answer an open question related to bisimilarity checking on labelled transition systems generated by prefix rewrite rules on words. Stirling (1996, 1998) proved the decidability of bisimilarity for normed pushdown processes. This result was substantially extended by Senizergues (1998, 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 Senizergues. 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 a a W ->(a) R and R-1 ->(a) R-2 and show when they yield low undecidability (Pi(0)(1)-completeness) and when high undecidability (Sigma(1)(1)-completeness), all with and without the assumption of normedness.
dc.identifier.doi 10.1007/11690634
dc.identifier.wos 000237082000019

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