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14
On the Bisimulation Proof Method
 JOURNAL OF MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 1994
"... The most popular method for establishing bisimilarities among processes is to exhibit bisimulation relations. By definition, R is a bisimulation relation if R progresses to R itself, i.e., pairs of processes in R can match each other's actions and their derivatives are again in R. We study generali ..."
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Cited by 72 (2 self)
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The most popular method for establishing bisimilarities among processes is to exhibit bisimulation relations. By definition, R is a bisimulation relation if R progresses to R itself, i.e., pairs of processes in R can match each other's actions and their derivatives are again in R. We study generalisations of the method aimed at reducing the size of the relations to exhibit and hence relieving the proof work needed to establish bisimilarity results. We allow a relation R to progress to a different relation F(R), where F is a function on relations. Functions which can be safely used in this way (i.e., such that if R progresses to F(R), then R only includes pairs of bisimilar processes) are sound. We give a simple condition which ensures soundness. We show that the class of sound functions contains nontrivial functions and we study the closure properties of the class w.r.t. various important function constructors, like composition, union and iteration. These properties allow us to cons...
Verification on Infinite Structures
, 2000
"... In this chapter, we present a hierarchy of infinitestate systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonlystudied classes of systems such as contextfree and pushdown automata, and Petri net processes. We then examine the ..."
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Cited by 69 (2 self)
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In this chapter, we present a hierarchy of infinitestate systems based on the primitive operations of sequential and parallel composition; the hierarchy includes a variety of commonlystudied classes of systems such as contextfree and pushdown automata, and Petri net processes. We then examine the equivalence and regularity checking problems for these classes, with special emphasis on bisimulation equivalence, stressing the structural techniques which have been devised for solving these problems. Finally, we explore the model checking problem over these classes with respect to various linear and branchingtime temporal logics.
Bisimulation Collapse and the Process Taxonomy
, 1996
"... . We consider the factorization (collapse) of infinite transition graphs wrt. bisimulation equivalence. It turns out that almost none of the more complex classes of the process taxonomy, which has been established in the last years, are preserved by this operation. However, for the class of BPA grap ..."
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Cited by 39 (1 self)
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. We consider the factorization (collapse) of infinite transition graphs wrt. bisimulation equivalence. It turns out that almost none of the more complex classes of the process taxonomy, which has been established in the last years, are preserved by this operation. However, for the class of BPA graphs (i.e. prefix transition graphs of contextfree grammars) we can show that the factorization is effectively a regular graph, i.e. finitely representable by means of a deterministic hypergraph grammar. Since finiteness of regular graphs is decidable, this yields, as a corollary, a decision procedure for the finiteness problem of contextfree processes wrt. bisimulation equivalence. 1 Introduction In concurrency theory, process calculi are widely accepted as algebraic description languages for concurrent systems. Their semantics are usually formulated in terms of labelled transition graphs which model the dynamic behaviour together with some notion of behavioural equivalence. Since there is...
Undecidable Equivalences for Basic Parallel Processes
 13th Conference on Foundations of Software Technology and Theoretical Computer Science
, 1993
"... . Recent results show that strong bisimilarity is decidable for the class of Basic Parallel Processes (BPP), which corresponds to the subset of CCS definable using recursion, action prefixing, nondeterminism and the full merge operator. In this paper we examine all other equivalences in the linear/b ..."
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Cited by 25 (2 self)
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. Recent results show that strong bisimilarity is decidable for the class of Basic Parallel Processes (BPP), which corresponds to the subset of CCS definable using recursion, action prefixing, nondeterminism and the full merge operator. In this paper we examine all other equivalences in the linear/branching time hierarchy [12] and show that none of them are decidable for BPP. 1 Introduction Much attention has been devoted to the study of process calculi and in particular to behavioural semantics for these calculi. In order to capture the behavioural aspects of processes, a variety of equivalences have been proposed. Various criteria exist for comparing the merits and deficiencies of these equivalences. A systematic approach consists of classifying the equivalences according to their coarseness. For this purpose van Glabbeek proposed the linear/branching time spectrum which is illustrated in Figure 1 [12]. The least discriminating equivalences are at the bottom of the diagram. Arrows i...
An Elementary Bisimulation Decision Procedure for Arbitrary ContextFree Processes
, 1994
"... We present an elementary algorithm for deciding bisimulation equivalence between arbitrary contextfree processes. This improves on the state of the art algorithm of Christensen, Huttel and Stirling consisting of two semidecision procedures running in parallel, which prohibits any complexity est ..."
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Cited by 16 (2 self)
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We present an elementary algorithm for deciding bisimulation equivalence between arbitrary contextfree processes. This improves on the state of the art algorithm of Christensen, Huttel and Stirling consisting of two semidecision procedures running in parallel, which prohibits any complexity estimation. The point of our algorithm is the effective construction of a finite relation characterizing all bisimulation equivalence classes, whose mere existence was exploited for the above mentioned decidability result.
Weak bisimilarity with infinitestate systems can be decided in polynomial time
 In Proc. of CONCUR'99, volume 1664 of LNCS
, 1999
"... Abstract. We prove that weak bisimilarity is decidable in polynomial time between BPA and finitestate processes, and between normed BPP and finitestate processes. To the best of our knowledge, these are the first polynomial algorithms for weak bisimilarity with infinitestate systems. 1 ..."
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Cited by 7 (4 self)
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Abstract. We prove that weak bisimilarity is decidable in polynomial time between BPA and finitestate processes, and between normed BPP and finitestate processes. To the best of our knowledge, these are the first polynomial algorithms for weak bisimilarity with infinitestate systems. 1
On the Completeness of the Equations for the Kleene Star in Bisimulation
 In Proceedings AMAST'96, LNCS 1101
, 1996
"... . A classical result from Redko [20] says that there does not exist a complete finite equational axiomatization for the Kleene star modulo trace equivalence. Fokkink and Zantema [13] showed, by means of a term rewriting analysis, that there does exist a complete finite equational axiomatization for ..."
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Cited by 7 (3 self)
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. A classical result from Redko [20] says that there does not exist a complete finite equational axiomatization for the Kleene star modulo trace equivalence. Fokkink and Zantema [13] showed, by means of a term rewriting analysis, that there does exist a complete finite equational axiomatization for the Kleene star up to strong bisimulation equivalence. This paper presents a simpler and shorter completeness proof. Furthermore, the result is extended to open terms, i.e., to !completeness. Finally, it is shown that the three equations for the Kleene star are all essential for completeness. 1 Introduction Kleene [15] defined a binary operator x y in the context of finite automata, which denotes the iterate of x on y. Intuitively, the expression x y can choose to execute either x, after which it evolves into x y again, or y, after which it terminates. An advantage of the Kleene star is that on the one hand it can express recursion, while on the other hand it can be captured in eq...
On the Decidability of Process Equivalences for the picalculus
, 1994
"... We present general results for showing process equivalences applied to the finite control fragment of the ßcalculus decidable. Firstly a Finite Reachability Theorem states that up to finite name spaces and up to a static normalisation procedure, the set of reachable agent expressions is finite. Sec ..."
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Cited by 5 (0 self)
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We present general results for showing process equivalences applied to the finite control fragment of the ßcalculus decidable. Firstly a Finite Reachability Theorem states that up to finite name spaces and up to a static normalisation procedure, the set of reachable agent expressions is finite. Secondly a Boundedness Lemma shows that no potential computations are missed when name spaces are chosen large enough, but finite. We show how these results lead to decidability for a number of ßcalculus equivalences such as strong or weak, late or early bismulation equivalence. Furthermore, for strong late equivalence we show how our techniques can be used to adapt the wellknown PaigeTarjan algorithm. Strikingly this results in a single exponential running time not much worse than the running time for the case of for instance CCS. Our results considerably strengthens previous results on decidable equivalences for parameterpassing process calculi. 1 Introduction The problem of obtaining ...
Checking NFA equivalence with bisimulations up to congruence
"... Abstract—We introduce bisimulation up to congruence as a technique for proving language equivalence of nondeterministic finite automata. Exploiting this technique, we devise an optimisation of the classical algorithm by Hopcroft and Karp [12] that, instead of computing the whole determinised automa ..."
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Cited by 5 (0 self)
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Abstract—We introduce bisimulation up to congruence as a technique for proving language equivalence of nondeterministic finite automata. Exploiting this technique, we devise an optimisation of the classical algorithm by Hopcroft and Karp [12] that, instead of computing the whole determinised automata, explores only a small portion of it. Although the optimised algorithm remains exponential in worst case (the problem is PSPACEcomplete), experimental results show improvements of several orders of magnitude over the standard algorithm. I.
SemiGroups Acting on ContextFree Graphs
"... Let \Gamma be some contextfree graph. We give sufficient conditions on a semigroup of bisimulations H ensuring that the quotient Hn\Gamma is contextfree. Using these sufficient conditions we show that the quotient Aut(\Gamma )n\Gamma of \Gamma by its full group of automorphisms is always context ..."
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Cited by 4 (0 self)
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Let \Gamma be some contextfree graph. We give sufficient conditions on a semigroup of bisimulations H ensuring that the quotient Hn\Gamma is contextfree. Using these sufficient conditions we show that the quotient Aut(\Gamma )n\Gamma of \Gamma by its full group of automorphisms is always contextfree. We then give examples showing optimality (in some sense) of the above result.