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46
WellStructured Transition Systems Everywhere!
 THEORETICAL COMPUTER SCIENCE
, 1998
"... Wellstructured transition systems (WSTS's) are a general class of infinite state systems for which decidability results rely on the existence of a wellquasiordering between states that is compatible with the transitions. In this article, we provide an extensive treatment of the WSTS idea and show ..."
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Cited by 197 (9 self)
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Wellstructured transition systems (WSTS's) are a general class of infinite state systems for which decidability results rely on the existence of a wellquasiordering between states that is compatible with the transitions. In this article, we provide an extensive treatment of the WSTS idea and show several new results. Our improved definitions allow many examples of classical systems to be seen as instances of WSTS's.
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.
Infinite state model checking by abstract interpretation and program specialisation
 LogicBased Program Synthesis and Transformation. Proceedings of LOPSTR’99, LNCS 1817
, 2000
"... Abstract. We illustrate the use of logic programming techniques for finite model checking of CTL formulae. We present a technique for infinite state model checking of safety properties based upon logic program specialisation and analysis techniques. The power of the approach is illustrated on severa ..."
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Cited by 55 (24 self)
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Abstract. We illustrate the use of logic programming techniques for finite model checking of CTL formulae. We present a technique for infinite state model checking of safety properties based upon logic program specialisation and analysis techniques. The power of the approach is illustrated on several examples. For that, the efficient tools logen and ecce are used. We discuss how this approach has to be extended to handle more complicated infinite state systems and to handle arbitrary CTL formulae. 1
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 43 (2 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.
Deciding BisimulationLike Equivalences with FiniteState Processes
, 1999
"... We show that characteristic formulae for nitestate systems up to bisimulationlike equivalences (e.g., strong and weak bisimilarity) can be given in the simple branchingtime temporal logic EF. Since EF is a very weak fragment of the modal µcalculus, model checking with EF is decidable for many mo ..."
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Cited by 41 (14 self)
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We show that characteristic formulae for nitestate systems up to bisimulationlike equivalences (e.g., strong and weak bisimilarity) can be given in the simple branchingtime temporal logic EF. Since EF is a very weak fragment of the modal µcalculus, model checking with EF is decidable for many more classes of infinitestate systems. This yields a general method for proving decidability of bisimulationlike equivalences between infinitestate processes and finitestate ones. We apply this method to the class of PAD processes, which strictly subsumes PA and pushdown (PDA) processes, showing that a large class of bisimulationlike equivalences (including, e.g., strong and weak bisimilarity) is decidable between PAD and finitestate processes. On the other hand, we also demonstrate that no `reasonable' bisimulationlike equivalence is decidable between stateextended PA processes and finitestate ones. Furthermore, weak bisimilarity with finitestate processes is shown to be undecidable even for state...
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...
Model checking multithreaded programs with asynchronous atomic methods
 In 18th International Conference on Computer Aided Verification (CAV’06). LNCS
, 2006
"... Abstract. In order to make multithreaded programming manageable, programmers often follow a design principle where they break the problem into tasks which are then solved asynchronously and concurrently on different threads. This paper investigates the problem of model checking programs that follow ..."
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Cited by 27 (5 self)
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Abstract. In order to make multithreaded programming manageable, programmers often follow a design principle where they break the problem into tasks which are then solved asynchronously and concurrently on different threads. This paper investigates the problem of model checking programs that follow this idiom. We present a programming language SPL that encapsulates this design pattern. SPL extends simplified form of sequential Java to which we add the capability of making asynchronous method invocations in addition to the standard synchronous method calls and the ability to execute asynchronous methods in threads atomically and concurrently. Our main result shows that the control state reachability problem for finite SPL programs is decidable. Therefore, such multithreaded programs can be model checked using the counterexample guided abstractionrefinement framework. 1
Solving Coverability Problems of Petri Nets by Partial Deduction
 Proceedings of PPDP’2000
, 2000
"... In recent work it has been shown that infinite state model checking can be performed by a combination of partial deduction of logic programs and abstract interpretation. This paper focuses on a particular class of problems  coverability for (infinite state) Petri nets  and shows how existing tech ..."
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Cited by 26 (17 self)
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In recent work it has been shown that infinite state model checking can be performed by a combination of partial deduction of logic programs and abstract interpretation. This paper focuses on a particular class of problems  coverability for (infinite state) Petri nets  and shows how existing techniques and tools for declarative programs can be successfully applied. In particular, we show that a restricted form of partial deduction is already powerful enough to decide all coverability properties of Petri Nets. We also prove that two particular instances of partial deduction exactly compute the KarpMiller tree as well as Finkel's minimal coverability set. We thus establish a link between algorithms for Petri nets and logic program specialisation.
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...