Undecidability of Bisimilarity by Defender's Forcing

JANČAR, Petr and Jiří SRBA. Undecidability of Bisimilarity by Defender's Forcing. Journal of the ACM. New York: ACM, 2008, 55/2008, No 1, p. 1-26. ISSN 0004-5411.

Basic information

• Original name: Undecidability of Bisimilarity by Defender's Forcing
• Name in Czech: Nerozhodnutelnost bisimulace pomoci tlaku obránce
• Authors: JANČAR, Petr (203 Czech Republic) and Jiří SRBA (203 Czech Republic, guarantor).
• Edition: Journal of the ACM, New York, ACM, 2008, 0004-5411.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10201 Computer sciences, information science, bioinformatics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• Impact factor: Impact factor: 2.339
• RIV identification code: RIV/00216224:14330/08:00026472
• Organization unit: Faculty of Informatics
• UT WoS: 000253939800005
• Keywords in English: undecidability; bisimilarity; rewrite systems
• Tags: bisimilarity, rewrite systems, undecidability
• Tags: International impact, Reviewed

Abstract

tirling (1996, 1998) proved the decidability of bisimilarity on so-called normed pushdown processes. This result was substantially extended by Senizergues(1998, 2005) who showed the decidability of bisimilarity for regular (or equational) graphs of finite out-degree; this essentially coincides with weak bisimilarity of processes generated by (unnormed) pushdown automata where the epsilon-transitions can only deterministically pop the stack. The question of decidability of bisimilarity for the more general class of so called Type -1 systems, which is equivalent to weak bisimilarity on unrestricted epsilon-popping pushdown processes, was left open. This was repeatedly indicated by both Stirling and Senizergues. Here we answer the question negatively, that is, we show the undecidability of bisimilarity on Type -1 systems, even in the normed case. We achieve the result by applying a technique we call Defender's Forcing, referring to the bisimulation games. The idea is simple, yet powerful. We demonstrate its versatility by deriving further results in a uniform way. First, we classify several versions of the undecidable problems for prefix rewrite systems (or pushdown automata) as Pi^0_1-complete or Sigma^1_1-complete. Second, we solve the decidability question for weak bisimilarity on PA (Process Algebra) processes, showing that the problem is undecidable and even Sigma^1_1-complete. Third, we show Sigma^1_1-completeness of weak bisimilarity for so-called parallel pushdown (or multiset) automata, a subclass of (labeled, place/transition) Petri nets.

Abstract (in Czech)

tirling (1996, 1998) proved the decidability of bisimilarity on so-called normed pushdown processes. This result was substantially extended by Senizergues(1998, 2005) who showed the decidability of bisimilarity for regular (or equational) graphs of finite out-degree; this essentially coincides with weak bisimilarity of processes generated by (unnormed) pushdown automata where the epsilon-transitions can only deterministically pop the stack. The question of decidability of bisimilarity for the more general class of so called Type -1 systems, which is equivalent to weak bisimilarity on unrestricted epsilon-popping pushdown processes, was left open. This was repeatedly indicated by both Stirling and Senizergues. Here we answer the question negatively, that is, we show the undecidability of bisimilarity on Type -1 systems, even in the normed case. We achieve the result by applying a technique we call Defender's Forcing, referring to the bisimulation games. The idea is simple, yet powerful. We demonstrate its versatility by deriving further results in a uniform way. First, we classify several versions of the undecidable problems for prefix rewrite systems (or pushdown automata) as Pi^0_1-complete or Sigma^1_1-complete. Second, we solve the decidability question for weak bisimilarity on PA (Process Algebra) processes, showing that the problem is undecidable and even Sigma^1_1-complete. Third, we show Sigma^1_1-completeness of weak bisimilarity for so-called parallel pushdown (or multiset) automata, a subclass of (labeled, place/transition) Petri nets.

Links

• MSM0021622419, plan (intention): Name: Vysoce paralelní a distribuované výpočetní systémy

Investor: Ministry of Education, Youth and Sports of the CR, Highly Parallel and Distributed Computing Systems