Undecidability Results for Bisimilarity on Prefix Rewrite Systems
2014
Abstract. We answer an open question related to bisimilarity check-ing 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 Sénizergues (1998, 2005) who showed the decidability for regular (or equational) graphs of finite out-degree (which include unnormed push-down 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 bisimilar-ity on Type-1 systems, even in the normed case. We complete the pic-ture 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 (Π01-completeness) and when high undecidability (Σ 1 1-completeness), all with and without the assumption of normedness. 1