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64
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
Decidability Issues for Petri Nets  a survey
, 1994
"... : We survey 25 years of research on decidability issues for Petri nets. We collect results on the decidability of important properties, equivalence notions, and temporal logics. 1. Introduction Petri nets are one of the most popular formal models for the representation and analysis of parallel proc ..."
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Cited by 90 (5 self)
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: We survey 25 years of research on decidability issues for Petri nets. We collect results on the decidability of important properties, equivalence notions, and temporal logics. 1. Introduction Petri nets are one of the most popular formal models for the representation and analysis of parallel processes. They are due to C.A. Petri, who introduced them in his doctoral dissertation in 1962. Some years later, and independently from Petri's work, Karp and Miller introduced vector addition systems [47], a simple mathematical structure which they used to analyse the properties of "parallel program schemata', a model for parallel computation. In their seminal paper on parallel program schemata, Karp and Miller studied some decidability issues for vector addition systems, and the topic continued to be investigated by other researchers. When Petri's ideas reached the States around 1970, it was observed that Petri nets and vector addition systems were mathematically equivalent, even though thei...
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.
Process Rewrite Systems
 INFORMATION AND COMPUTATION
, 1997
"... Many formal models for infinitestate concurrent systems are equivalent to special classes of rewrite systems. We classify these models by their expressiveness and define a hierarchy of classes of rewrite systems. We show that this hierarchy is strict with respect to bisimulation equivalence. The mo ..."
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Cited by 62 (9 self)
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Many formal models for infinitestate concurrent systems are equivalent to special classes of rewrite systems. We classify these models by their expressiveness and define a hierarchy of classes of rewrite systems. We show that this hierarchy is strict with respect to bisimulation equivalence. The most general and most expressive class of systems in this hierarchy is called Process Rewrite Systems (PRS). They subsume Petri nets, PAProcesses and pushdown processes and are strictly more expressive than any of these. Intuitively, PRS can be seen as an extension of Petri nets by subroutines that can return a value to their caller. We show that the reachability problem is decidable for PRS. It is even decidable if there is a reachable state that satisfies certain properties that can be encoded in a simple logic. Thus PRS are more expressive than Petri nets, but not Turingpowerful.
Decidability of Model Checking for InfiniteState Concurrent Systems
 Acta Informatica
"... We study the decidability of the model checking problem for linear and branching time logics, and two models of concurrent computation, namely Petri nets and Basic Parallel Processes. 1 Introduction Most techniques for the verification of concurrent systems proceed by an exhaustive traversal of the ..."
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Cited by 60 (1 self)
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We study the decidability of the model checking problem for linear and branching time logics, and two models of concurrent computation, namely Petri nets and Basic Parallel Processes. 1 Introduction Most techniques for the verification of concurrent systems proceed by an exhaustive traversal of the state space. Therefore, they are inherently incapable of considering systems with infinitely many states. Recently, some new methods have been developed in order to at least palliate this problem. Using them, several verification problems for some restricted infinitestate models have been shown to be decidable. These results can be classified into those showing the decidability of equivalence relations [8, 9, 24, 26], and those showing the decidability of model checking for different modal and temporal logics. In this paper, we contribute to this second group. The model checking problem has been studied so far for three infinitestate models: contextfree processes, pushdown processes, and...
Petri Nets, Commutative ContextFree Grammars, and Basic Parallel Processes
, 1997
"... . The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place. As a corollary, the reachability problem for this class is proved to be NPcomplete. Further consequences are: the uniform word problem for commutative co ..."
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Cited by 46 (6 self)
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. The paper provides a structural characterisation of the reachable markings of Petri nets in which every transition has exactly one input place. As a corollary, the reachability problem for this class is proved to be NPcomplete. Further consequences are: the uniform word problem for commutative contextfree grammars is NPcomplete; weakbisimilarity is semidecidable for Basic Parallel Processes. Keywords: Petri nets, Commutative Contextfree Grammars, Basic Parallel Processes, Weak bisimilarity. 1. Introduction The reachability problem plays a central role in Petri net theory, and has been studied in numerous papers (see [5] for a comprehensive list of references). In the first part of this paper we study it for the nets in which every transition needs exactly one token to occur. Following [8], we call them communicationfree nets, because no cooperation between places is needed in order to fire a transition; every transition is activated by one single token, and the tokens may flow...
Actions Speak Louder than Words: Proving Bisimilarity for ContextFree Processes
, 1991
"... Baeten, Bergstra, and Klop (and later Caucal) have proved the remarkable result that bisimulation equivalence is decidable for irredundant contextfree grammars. In this paper we provide a much simpler and much more direct proof of this result using a tableau decision method involving goaldirec ..."
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Cited by 45 (9 self)
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Baeten, Bergstra, and Klop (and later Caucal) have proved the remarkable result that bisimulation equivalence is decidable for irredundant contextfree grammars. In this paper we provide a much simpler and much more direct proof of this result using a tableau decision method involving goaldirected rules. The decision procedure also provides the essential part of the bisimulation relation between two processes which underlies their equivalence. We also show how to obtain a sound and complete sequentbased equational theory for such processes from the tableau system and how one can extract what Caucal calls a fundamental relation from a successful tableau.
The Regular Viewpoint on PAProcesses
 Theoretical Computer Science
, 1999
"... PA is the process algebra allowing nondeterminism, sequential and parallel compositions, and recursion. We suggest viewing PAprocesses as trees, and using treeautomata techniques for verification problems on PA. Our main result is that the set of iterated predecessors of a regular set of PAproce ..."
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Cited by 40 (1 self)
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PA is the process algebra allowing nondeterminism, sequential and parallel compositions, and recursion. We suggest viewing PAprocesses as trees, and using treeautomata techniques for verification problems on PA. Our main result is that the set of iterated predecessors of a regular set of PAprocesses is a regular tree language, and similarly for iterated successors. Furthermore, the corresponding treeautomata can be built effectively in polynomialtime. This has many immediate applications to verification problems for PAprocesses, among which a simple and general modelchecking algorithm.
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...
More Infinite Results
, 1997
"... Recently there has been a spurt of activity in concurrency theory centred on the analysis of infinitestate systems. The following two problems have been intensely investigated: (1) given two infinitestate systems, are they equal with respect to a certain equivalence notion?, and (2) given an infin ..."
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Cited by 38 (2 self)
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Recently there has been a spurt of activity in concurrency theory centred on the analysis of infinitestate systems. The following two problems have been intensely investigated: (1) given two infinitestate systems, are they equal with respect to a certain equivalence notion?, and (2) given an infinitestate system and a property expressed in a certain temporal logic, does the system satisfy the property? In his paper "Infinite Results" [Mol96] , Moller surveys some of the key results on the decidability and complexity of problem (1). This paper is a survey on the results about problem (2). 1 Introduction Most techniques for the verification of concurrent systems proceed by an exhaustive traversal of the state space. Therefore, they are inherently incapable of considering systems with infinitely many states. Recently, some methods have been developed to overcome this limitation, at least for restricted classes of infinitestate systems. Using them, several verification problems have b...