Undecidability Results for Bisimilarity on Prefix Rewrite Systems

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Název česky Nerozhodnutelnost Bisimulace na Prefixovych Prepisovacich Systemech
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JANČAR Petr SRBA Jiří

Rok publikování 2006
Druh Článek v odborném periodiku
Časopis / Zdroj LNCS, Foundations of Software Science and Computation Structures (FOSSACS'06)
Fakulta / Pracoviště MU

Fakulta informatiky

Citace
Obor Informatika
Klíčová slova bisimilarity; undecidability; prefix rewriting
Popis 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 w -a-> R and R1 -a-> R2 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.
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