An elementary bisimulation decision procedure for arbitrary context-free processes

Burkart, Olaf; Caucal, Didier; Steffen, Bernhard

doi:10.1007/3-540-60246-1_148

Cited by 59 publications

(45 citation statements)

References 8 publications

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“…An interesting subclass is BPA (Basic Process Algebra), corresponding to real-time PDA with a single control state. In the so called normed case bisimilarity is polynomial (see the above mentioned [13], [8]), but in general bisimilarity is in 2-ExpTime (claimed in [6] and explicitly proven in [16]) and ExpTime-hard [17].…”

Section: Related Work and Some Open Questionsmentioning

confidence: 99%

Equivalences of Pushdown Systems Are Hard

Jancar

2014

Lecture Notes in Computer Science

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Abstract. Language equivalence of deterministic pushdown automata (DPDA) was shown to be decidable by Sénizergues (1997Sénizergues ( , 2001Stirling (2002) then showed that the problem is primitive recursive.Sénizergues (1998, 2005) also generalized his proof to show decidability of bisimulation equivalence of (nondeterministic) PDA where ε-rules can be only deterministic and popping; this problem was shown to be nonelementary by Benedikt, Göller, Kiefer, and Murawski (2013), even for PDA with no ε-rules.Here we refine Stirling's analysis and show that DPDA equivalence is in TOWER, i.e., in the "least" nonelementary complexity class. The basic proof ideas remain the same but the presentation and the analysis are simplified, in particular by using a first-order term framework.The framework of (nondeterministic) first-order grammars, with term root-rewriting rules, is equivalent to the model of PDA with restricted ε-rules to which Sénizergues's decidability proof applies. We show that bisimulation equivalence is here Ackermann-hard, and thus not primitive recursive.

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Section: Related Work and Some Open Questionsmentioning

confidence: 99%

Equivalences of Pushdown Systems Are Hard

Jancar

2014

Lecture Notes in Computer Science

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“…Without this restriction Lemma 3.18 does not hold. In [BCS95] an ingenious counter example to that extent is given. Based on it, Bernhard Steffen supplied us a specification of a process name which is not weakly normed repeat invariant, i.e.…”

Section: Theorem 316mentioning

confidence: 99%

“…If we want to use our criterion of weakly normed repeat invariance, this involves checking bisimulation equivalence between perpetual context-free processes 7 . Checking bisimulation equivalence of normed processes is known to have a polynomial time complexity [HM95], whereas the complexity of checking bisimulation of arbitrary context-free processes is (doubly) exponential [BCS95].…”

Section: Con CL Us Ionsmentioning

confidence: 99%

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Regularity for a large class of context-free processes is decidable

Bosscher

Griffioen

1996

Automata, Languages and Programming

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Abstract. Regularity of context-free processes has been proved to be decidable for BPA systems by [MM94] and normed context-free processes by [Kru95). In this paper the decidable class of regular context-free processes is enlarged to that of context-free processes over so-called NRD specifications (definition in the paper). Furthermore an upper bound is given for the number of states modulo bisimulation.

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“…Simpler proofs have been given later in [18,13], and there is even a polynomial-time algorithm [15]. The decidability result has later been extended to the class of all (not necessarily normed) BPA processes in [9], but the best known algorithm is doubly exponential [4]. Decidability of strong bisimilarity for BPP processes has been established in [8], but the algorithm has non-elementary complexity.…”

Section: Introductionmentioning

confidence: 99%