2026-07-22T01:28:53Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7783 2024-03-06T10:41:07Z ddc:004 open_access

Coverability Synthesis in Parametric Petri Nets David, Nicolas Jard, Claude Lime, Didier Roux, Olivier H. Petri net Parameters Coverability Unboundedness Synthesis We study Parametric Petri Nets (PPNs), i.e., Petri nets for which some arc weights can be parameters. In that setting, we address a problem of parameter synthesis, which consists in computing the exact set of values for the parameters such that a given marking is coverable in the instantiated net. Since the emptiness of that solution set is already undecidable for general PPNs, we address a special case where parameters are used only as input weights (preT-PPNs), and consequently for which the solution set is downward-closed. To this end, we invoke a result for the representation of upward closed set from Valk and Jantzen. To use this procedure, we show we need to decide universal coverability, that is decide if some marking is coverable for every possible values of the parameters. We therefore provide a proof of its EXPSPACE-completeness, thus settling the previously open problem of its decidability. 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, that is decide if there exists values of the parameters making a given marking coverable. This problem is known decidable but we provide here a cleaner proof, providing its EXPSPACE-completeness, by reduction to Omega Petri Nets. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Nicolas David and Claude Jard and Didier Lime and Olivier H. Roux 2017 Is Part Of LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CONCUR.2017.14 urn:nbn:de:0030-drops-77831 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.14 eng https://creativecommons.org/licenses/by/3.0/legalcode