Decidability of reachability in vector addition systems (Preliminary Version)

Kosaraju, S. Rao

doi:10.1145/800070.802201

Cited by 279 publications

(204 citation statements)

References 4 publications

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“…So, a VASS can be represented by a tuple V = Q, n, δ where Q is the finite set of control states and δ is a finite subset of Q × Z n × Q. A famous result states that the reachability problem for VASS is decidable [May84,Kos82,Ler09]. It has been the subject of the book [Reu90] and its proof requires many non-trivial steps involving graph theory, logic and theory of well-quasi-orderings.…”

Section: Some Classes Of Presburger Counter Systemsmentioning

confidence: 99%

Witness Runs for Counter Machines

Barrett

Demri

Deters

2013

Frontiers of Combining Systems

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Abstract. In this paper, we present recent results about the verification of counter machines by using decision procedures for Presburger arithmetic. We recall several known classes of counter machines for which the reachability sets are Presburger-definable as well as temporal logics with arithmetical constraints. We discuss issues related to flat counter machines, path schema enumeration, and the use of SMT solvers.

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Section: Some Classes Of Presburger Counter Systemsmentioning

confidence: 99%

Witness Runs for Counter Machines

Barrett

Demri

Deters

2013

Frontiers of Combining Systems

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“…We establish this by a reduction to the zero reachability problem for Petri nets, as defined in Section 4, which is decidable [17,16]. The representation of finite tree automatas as Petri nets was studied in [25].…”

Section: ) L(amentioning

confidence: 99%

Behavioural Equivalence for Infinite Systems—Partially Decidable!

Nielsen¹,

Sunesen²

1995

BRICS

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For finite-state systems non-interleaving equivalences are computationally at least as hard as interleaving equivalences. In this paper we show that when moving to infinite-state systems, this situation may change dramatically.We compare standard language equivalence for process description languages with two generalizations based on traditional approaches capturing non-interleaving behaviour, pomsets representing global causal dependency, and locality representing spatial distribution of events.We first study equivalences on Basic Parallel Processes, BPP, a process calculus equivalent to communication free Petri nets. For this simple process language our two notions of non-interleaving equivalences agree. More interestingly, we show that they are decidable, contrasting a result of Hirshfeld that standard interleaving language equivalence is undecidable. Our result is inspired by a recent result of Esparza and Kiehn, showing the same phenomenon in the setting of model checking.We follow up investigating to which extent the result extends to larger subsets of CCS and TCSP. We discover a significant difference between our non-interleaving equivalences. We show that for a certain non-trivial subclass of processes between BPP and TCSP, not only are the two equivalences different, but one (locality) is decidable whereas the other (pomsets) is not. The decidability result for locality is proved by a reduction to the reachability problem for Petri nets.

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“…For place/transition Petri nets (which may have infinitely many states), it is one of the hardest decision problems known among the naturally emerging yet decidable problems in computer science. General solutions have been found by Mayr [14] and Kosaraju [9] with later simplifications made by Lambert [11], but there are complexity issues. All these approaches use coverability graphs which can have a non-primitive-recursive size with respect to the corresponding Petri net.…”

Section: Introductionmentioning

confidence: 99%

Applying CEGAR to the Petri Net State Equation

Wimmel

Wolf

2011

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. We propose a reachability verification technique that combines the Petri net state equation (a linear algebraic overapproximation of the set of reachable states) with the concept of counterexample guided abstraction refinement. In essence, we replace the search through the set of reachable states by a search through the space of solutions of the state equation. We demonstrate the excellent performance of the technique on several real-world examples. The technique is particularly useful in those cases where the reachability query yields a negative result: While state space based techniques need to fully expand the state space in this case, our technique often terminates promptly. In addition, we can derive some diagnostic information in case of unreachability while state space methods can only provide witness paths in the case of reachability.

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Decidability of reachability in vector addition systems (Preliminary Version)

Abstract: A convincing proof of the decidability of reachability in vector addition systems is presented.No drastically new ideas beyond those in Sacerdote and Tenney, and Mayr are made use of. The complicated tree constructions in the earlier proofs are completely eliminated.

Cited by 279 publications

References 4 publications

Witness Runs for Counter Machines

Witness Runs for Counter Machines

Behavioural Equivalence for Infinite Systems—Partially Decidable!

Applying CEGAR to the Petri Net State Equation

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