JANČAR, Petr and Jiří SRBA. Undecidability Results for Bisimilarity on Prefix Rewrite Systems. LNCS, Foundations of Software Science and Computation Structures (FOSSACS'06), Netherlands: Spinger-Verlag, 2006, vol. 2006, No 3921, p. 277-291.
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Basic information
Original name Undecidability Results for Bisimilarity on Prefix Rewrite Systems
Name in Czech Nerozhodnutelnost Bisimulace na Prefixovych Prepisovacich Systemech
Authors JANČAR, Petr (203 Czechia) and Jiří SRBA (203 Czechia, guarantor).
Edition LNCS, Foundations of Software Science and Computation Structures (FOSSACS'06), Netherlands, Spinger-Verlag, 2006.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10201 Computer sciences, information science, bioinformatics
Country of publisher Netherlands
Confidentiality degree is not subject to a state or trade secret
RIV identification code RIV/00216224:14330/06:00015979
Organization unit Faculty of Informatics
UT WoS 000237082000019
Keywords in English bisimilarity; undecidability; prefix rewriting
Tags bisimilarity, prefix rewriting, undecidability
Tags International impact, Reviewed
Changed by Changed by: RNDr. JUDr. Vladimír Šmíd, CSc., učo 1084. Changed: 6/7/2007 09:01.
Abstract
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.
Abstract (in Czech)
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.
Links
GA201/03/1161, research and development projectName: Verifikace nekonečně stavových systémů
Investor: Czech Science Foundation, Standard Projects
MSM 143300001, plan (intention)Name: Nesekvenční modely výpočtů - kvantové a souběžné distribuované modely výpočetních procesů
Investor: Ministry of Education, Youth and Sports of the CR, Research Intents
MSM0021622419, plan (intention)Name: Vysoce paralelní a distribuované výpočetní systémy
Investor: Ministry of Education, Youth and Sports of the CR, Research Intents
1M0545, research and development projectName: Institut Teoretické Informatiky
Investor: Ministry of Education, Youth and Sports of the CR, Research Centres (National Research Programme)
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