Discrete Parameters in Petri Nets

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.
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Submitted on : Thursday, March 1, 2018 - 2:51:13 PM
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Nicolas David. Discrete Parameters in Petri Nets. Formal Languages and Automata Theory [cs.FL]. Université de Nantes Faculté des sciences et des techniques, 2017. English. ⟨tel-01720706⟩



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