2008
Undecidability of Bisimilarity by Defender's Forcing
JANČAR, Petr a Jiří SRBAZákladní údaje
Originální název
Undecidability of Bisimilarity by Defender's Forcing
Název česky
Nerozhodnutelnost bisimulace pomoci tlaku obránce
Autoři
JANČAR, Petr (203 Česká republika) a Jiří SRBA (203 Česká republika, garant)
Vydání
Journal of the ACM, New York, ACM, 2008, 0004-5411
Další údaje
Jazyk
angličtina
Typ výsledku
Článek v odborném periodiku
Obor
10201 Computer sciences, information science, bioinformatics
Stát vydavatele
Spojené státy
Utajení
není předmětem státního či obchodního tajemství
Impakt faktor
Impact factor: 2.339
Kód RIV
RIV/00216224:14330/08:00026472
Organizační jednotka
Fakulta informatiky
UT WoS
000253939800005
Klíčová slova anglicky
undecidability; bisimilarity; rewrite systems
Štítky
Příznaky
Mezinárodní význam, Recenzováno
Změněno: 29. 9. 2008 22:32, Prof. Jiří Srba, Ph.D.
V originále
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.
Česky
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.
Návaznosti
| MSM0021622419, záměr |
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