Some decision problems related to the reachability problem for Petri nets

Araki, Toshiro; Kasami, Tadao

doi:10.1016/0304-3975(76)90067-0

Cited by 89 publications

(57 citation statements)

References 4 publications

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“…Some of them, such as Coloured Petri nets [Jensen, 1987] are equivalent 5 to Petri nets and focus on improving the modelling capability whereas some others are more expressive. Indeed, some formalisms o er to use arcs with specific behaviours such as reset arcs [Araki and Kasami, 1976] or inhibitor arcs [Agerwala andFlynn, 1973, Hack, 1976], to add time to the model [Ramchandani, 1973, Merlin, 1974, Berthomieu and Diaz, 1991 on transitions, on places or on arcs (see [Boyer and Roux, 2008] for a comparison of those formalisms) or to consider real numbers markings [David and Alla, 1987].…”

Section: Notable Petri Nets Extensionsmentioning

confidence: 99%

Discrete Parameters in Petri Nets

David

Jard

Lime

et al. 2015

Application and Theory of Petri Nets and Concurrency

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Short abstract:With the aim of increasing the modelling capability of Petri nets, we suggest that models involve parameters to represent the weights of arcs, or the number of tokens in places. We consider the property of coverability of markings. Two general questions arise, the universal and the existential one: "Is there a parameter value for which the property is satisfied?" and "Does the property hold for all possible values of the parameters". We show that these issues are undecidable in the general case. Therefore, we also define subclasses of parameterised nets, depending on whether the parameters are used on places, input or output arcs of transitions. For some classes, we prove that universal and existential coverability become decidable, making these classes more usable in practice. To complete this study, we prove that those problems are ExpSpace-complete. We also address a problem of parameter synthesis, that is computing the set of values for the parameters such that a given marking is coverable in the instantiated net. Restricting parameters to only input weights (preT-PPNs) provides a downward-closed structure to the solution set. We therefore invoke a result for the representation of upward closed set from Valk and Jantzen. The condition to use this procedure is equivalent to decide the universal coverability. We also propose an adaptation of this reasoning to the case of parameters used only as output weights (postT-PPNs). In this case, the condition to use this procedure can be reduced to the decidability of the existential coverability. Finally, we broaden this study by establishing decision frontiers through the study of existential and universal reachability.Keywords: Petri nets -Parameters -Synthesis -Decidability -Complexity -CoverabilityReachability 6 Réseaux de Petri à Paramètres DiscretsRésumé court : Afin de permettre une modélisation plus souple des systèmes, nous proposons d'étendre les réseaux de Petri par des paramètres discrets représentant le poids des arcs ou le nombre de jetons présents dans les places. Dans ce modèle, tout problème de décision peut être décliné sous deux versions, une universelle, demandant si la propriété considérée est vraie quelles que soient les valeurs que prennent les paramètres et une existentielle, qui s'interroge sur l'existence d'une valeur pour les paramètres telle que la propriété soit satisfaite. Concernant la couverture, nous montrons que ces deux problèmes sont indécidables dans le cas général. Nous introduisons donc des sous classes syntaxiques basées sur la restriction des paramètres aux places, aux arcs en sortie ou aux arcs en entrée des transitions. Dans ces di érents cas, nous montrons que la couverture existentielle et universelle sont décidables et EXPSPACE-complètes. Nous étudions alors le problème de la synthèse de paramètres qui s'intéresse à calculer l'ensemble des valeurs de paramètres telles que la propriété considérée soit vraie. Sur les sous classes introduites, concernant la couverture, nous montrons que les ensembles solutions ...

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Section: Notable Petri Nets Extensionsmentioning

confidence: 99%

Discrete Parameters in Petri Nets

David

Jard

Lime

et al. 2015

Application and Theory of Petri Nets and Concurrency

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“…While solution to such a problem can perhaps be used gainfully in many purely theoretical areas like mathematics, computer science, universal algebra and order theory, decision theory [2], the extent and effectiveness of its utility in solving the practical problem requiring the design of multi-functional switches for the operation of certain discrete dynamical systems of common use such as washing machines and teleprinters (e.g., see [1,7,10]) can be explored instantly. So, the characterization of Boolean Petri nets is an open problem.…”

Section: Conclusion and Scopementioning

confidence: 99%

On the Problem of Characterizing Boolean Petri Nets

Kansal¹,

Singh²,

Acharya³

2015

IJCA

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Petri nets are used for describing, designing and studying discrete event-driven systems that are characterized as being concurrent, asynchronous, distributed, parallel, and/or nondeterministic. As a graphical tool, Petri net can be used for planning and designing a system with given objectives, more effectively than flowcharts and block diagrams. As a mathematical tool, it enables one to set up state equations and algebraic equations and other mathematical models which govern the behavior of systems. The aim of this paper is to present some basic results and necessary and sufficient condition for a 1-safe Petri net that generates all the binary nvectors as marking vectors, we shall call such Petri nets as Boolean Petri nets.

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“…The fact is that it does not behave as nicely as the classical definition (see below). However, it is a natural option with some extensions like VASSes extended with resets as in [2,8], or with nested zero-tests as in [27]. Proof.…”

Section: Weakly Computingmentioning

confidence: 99%