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58
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 113 (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...
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 97 (17 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 86 (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.
Algorithmic analysis of programs with well quasiordered domains
 Information and Computation
"... Over the past few years increasing research effort has been directed towards the automatic verification of infinitestate systems. This paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability. We present decidability res ..."
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Cited by 68 (17 self)
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Over the past few years increasing research effort has been directed towards the automatic verification of infinitestate systems. This paper is concerned with identifying general mathematical structures which can serve as sufficient conditions for achieving decidability. We present decidability results for a class of systems (called wellstructured systems) which consist of a finite control part operating on an infinite data domain. The results assume that the data domain is equipped with a preorder which is a well quasiordering, such that the transition relation is ``monotonic' ' (a simulation) with respect to the preorder. We show that the following properties are decidable for wellstructured systems: v Reachability: whether a certain set of control states is reachable. Other safety properties can be reduced to the reachability problem. 1
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 64 (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...
Undecidable Verification Problems for Programs with Unreliable Channels
 Information and Computation
, 1994
"... We consider the verification of a particular class of infinitestate systems, namely systems consisting of finitestate processes that communicate via unbounded lossy FIFO channels. This class is able to model e.g. link protocols such as the Alternating Bit Protocol and HDLC. In an earlier paper, we ..."
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Cited by 62 (13 self)
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We consider the verification of a particular class of infinitestate systems, namely systems consisting of finitestate processes that communicate via unbounded lossy FIFO channels. This class is able to model e.g. link protocols such as the Alternating Bit Protocol and HDLC. In an earlier paper, we showed that the problems of checking reachability, safety properties, and eventuality properties are decidable for this class of systems. In this paper, we show that the following problems are undecidable, namely ffl The model checking problem in propositional temporal logics such as Propositional Linear Time Temporal Logic (PTL) and Computation Tree Logic (CTL). ffl The problem of deciding eventuality properties with fair channels: do all computations eventually reach a given set of states if the unreliable channels satisfy fairness assumptions. The results are obtained through a reduction from a variant of Post's Correspondence Problem. This research report is a revised and extended ...
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 60 (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...
Undecidable Problems in Unreliable Computations
 THEORETICAL COMPUTER SCIENCE
, 2000
"... Lossy counter machines are defined as Minsky ncounter machines where the values in the counters can spontaneously decrease at any time. While termination is decidable for lossy counter machines, structural termination (termination for every input) is undecidable. This undecidability result has f ..."
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Cited by 57 (3 self)
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Lossy counter machines are defined as Minsky ncounter machines where the values in the counters can spontaneously decrease at any time. While termination is decidable for lossy counter machines, structural termination (termination for every input) is undecidable. This undecidability result has far reaching consequences. Lossy counter machines can be used as a general tool to prove the undecidability of many problems, for example (1) The verification of systems that model communication through unreliable channels (e.g. model checking lossy fifochannel systems and lossy vector addition systems). (2) Several problems for reset Petri nets, like structural termination, boundedness and structural boundedness. (3) Parameterized problems like fairness of broadcast communication protocols.
Bisimulation equivalence is decidable for normed Process Algebra
 Proceedings of ICALP'99, to appear, Lecture Notes in Computer Science
, 1999
"... We present a procedure for deciding whether two normed PA terms are bisimilar. The procedure is \elementary, " having doubly exponential nondeterministic time complexity. ..."
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Cited by 31 (0 self)
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We present a procedure for deciding whether two normed PA terms are bisimilar. The procedure is \elementary, " having doubly exponential nondeterministic time complexity.