Results 1  10
of
21
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 ..."
Abstract

Cited by 90 (5 self)
 Add to MetaCart
: 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 ..."
Abstract

Cited by 69 (2 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 45 (9 self)
 Add to MetaCart
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.
Undecidability of Bisimilarity for Petri Nets and Some Related Problems
, 1995
"... The main result shows the undecidability of (strong) bisimilarity for labelled (place / transition) Petri nets. The technique of the proof applies to the language (or trace) equivalence and the reachability set equality as well, which yields stronger versions with simpler proofs of already known ..."
Abstract

Cited by 45 (3 self)
 Add to MetaCart
The main result shows the undecidability of (strong) bisimilarity for labelled (place / transition) Petri nets. The technique of the proof applies to the language (or trace) equivalence and the reachability set equality as well, which yields stronger versions with simpler proofs of already known results. The paper also contains two decidability results. One concerns the Petri nets which are deterministic up to bisimilarity, the other concerns semilinear bisimulations and extends the result of [4] for Basic Parallel Processes. 1 Introduction The topic of the paper belongs to an interesting area in the theory of parallelism and concurrency, namely to the area of decidability questions for behavioural equivalences in various classes of (models of) processes. These questions are among the rst ones to ask when developing automated verication methods, for example. There is a large amount of equivalences in the literature (cf. e.g. [9]), nevertheless some of them are felt to be mor...
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 ..."
Abstract

Cited by 24 (7 self)
 Add to MetaCart
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...
Decidability issues for Petri nets
 Petri Nets Newsletter
, 1994
"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS ..."
Abstract

Cited by 19 (0 self)
 Add to MetaCart
Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent publications in the BRICS Report Series. Copies may be obtained by contacting: BRICS
The Joys of Bisimulation
, 1998
"... this paper we review results about bisimulation, from both the point of view of automata and from a logical point of view. We also consider how bisimulation has a role in finite model theory, and we offer a new undefinability result. ..."
Abstract

Cited by 17 (0 self)
 Add to MetaCart
this paper we review results about bisimulation, from both the point of view of automata and from a logical point of view. We also consider how bisimulation has a role in finite model theory, and we offer a new undefinability result.
Nested Semantics over Finite Trees are Equationally Hard
, 2003
"... This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied ..."
Abstract

Cited by 15 (11 self)
 Add to MetaCart
This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied in this paper, the collection of sound, closed (in)equations over a singleton action set is not finitely based.
Equality and Monodic FirstOrder Temporal Logic
 Studia Logica
, 2002
"... It has been shown recently that monodic firstorder temporal logic without functional symbols but with equality is incomplete, i.e. the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic twovari ..."
Abstract

Cited by 14 (7 self)
 Add to MetaCart
It has been shown recently that monodic firstorder temporal logic without functional symbols but with equality is incomplete, i.e. the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic twovariable formulae is not recursively enumerable.
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, ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
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.