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18
Bisimulation Equivalence is Decidable for all ContextFree Processes
 Information and Computation
, 1995
"... Introduction Over the past decade much attention has been devoted to the study of process calculi such as CCS, ACP and CSP [13]. Of particular interest has been the study of the behavioural semantics of these calculi as given by labelled transition graphs. One important question is when processes c ..."
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Cited by 92 (15 self)
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Introduction Over the past decade much attention has been devoted to the study of process calculi such as CCS, ACP and CSP [13]. Of particular interest has been the study of the behavioural semantics of these calculi as given by labelled transition graphs. One important question is when processes can be said to exhibit the same behaviour, and a plethora of behavioural equivalences exists today. Their main rationale has been to capture behavioural aspects that language or trace equivalences do not take into account. The theory of finitestate systems and their equivalences can now be said to be wellestablished. There are many automatic verification tools for their analysis which incorporate equivalence checking. Sound and complete equational theories exist for the various known equivalences, an elegant example is [18]. One may be led to wonder what the results will look like for infinitestate systems. Although language equivalence is decidable
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...
Decidability of Bisimulation Equivalence for Normed Pushdown Processes
 Theoretical Computer Science
, 1996
"... We prove that bisimulation equivalence is decidable for normed pushdown processes. 1 Introduction In the classical theory of automata the expressive power of pushdown automata is matched by contextfree grammars. Both accept the same family of languages, the contextfree languages. Concurrency theo ..."
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Cited by 24 (7 self)
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We prove that bisimulation equivalence is decidable for normed pushdown processes. 1 Introduction In the classical theory of automata the expressive power of pushdown automata is matched by contextfree grammars. Both accept the same family of languages, the contextfree languages. Concurrency theory requires a more intensional exposition of behaviour (as language equivalence need not be preserved in the presence of communicating abstract machines). Many finer equivalences have been proposed. Bisimulation equivalence, due to Park and Milner, has received much attention. Baeten, Bergstra and Klop proved that bisimulation equivalence is decidable for irredundant contextfree grammars (without the empty production) . Within process calculus theory these grammars correspond to normed BPA processes. Their proof relies on isolating a complex periodicity from the transition graphs of these processes. Simpler proofs of the result soon followed which expose algebraic structure. Caucal and Monf...
Regularity is Decidable for Normed PA Processes in Polynomial Time
, 1996
"... A process # is regular if it is bisimilar to a process # # with finitely many states. We prove that regularity of normed PA processes is decidable and we present a practically usable polynomialtime algorithm. Moreover, if the tested normed PA process # is regular then the process # # can be ..."
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Cited by 18 (3 self)
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A process # is regular if it is bisimilar to a process # # with finitely many states. We prove that regularity of normed PA processes is decidable and we present a practically usable polynomialtime algorithm. Moreover, if the tested normed PA process # is regular then the process # # can be e#ectively constructed. It implies decidability of bisimulation equivalence for any pair of processes such that one process of this pair is a normed PA process and the other process has finitely many states.
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.
Decidable Subsets of CCS
"... CCS is a universal formalism: any computable function is computed by some CCS agent. Moreover, one can reduce the halting problem for Turing machines to the problem of deciding bisimilarity of two CCS agents, thus demonstrating the undecidability of the equivalence checking problem. In this paper, ..."
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Cited by 14 (0 self)
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CCS is a universal formalism: any computable function is computed by some CCS agent. Moreover, one can reduce the halting problem for Turing machines to the problem of deciding bisimilarity of two CCS agents, thus demonstrating the undecidability of the equivalence checking problem. In this paper, we demonstrate the limits of decidability of CCS. In particular, we show that by simply disallowing either of communication or both restriction and relabelling, we arrive at a sublanguage which still describes a rich class of infinite state systems but for which bisimulation is decidable. We also demonstrate complete axiomatisations for these sublanguages. We compare these results with the undecidability of all other common equivalences.
A polynomialtime algorithm for deciding bisimulation equivalence of normed Basic Parallel Processes
, 1996
"... A polynomialtime algorithm is presented for deciding bisimulation equivalence of socalled Basic Parallel Processes: multisets of elementary processes combined by a commutative parallelcomposition operator. ..."
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Cited by 8 (1 self)
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A polynomialtime algorithm is presented for deciding bisimulation equivalence of socalled Basic Parallel Processes: multisets of elementary processes combined by a commutative parallelcomposition operator.
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