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Bounded Petri Net Synthesis from Modal Transition Systems is Undecidable

Author Uli Schlachter

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Uli Schlachter

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Uli Schlachter. Bounded Petri Net Synthesis from Modal Transition Systems is Undecidable. In 27th International Conference on Concurrency Theory (CONCUR 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 59, pp. 15:1-15:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.CONCUR.2016.15

Abstract

In this paper, the synthesis of bounded Petri nets from deterministic modal transition systems is shown to be undecidable.  The proof is built from three components.  First, it is shown that the problem of synthesising bounded Petri nets satisfying a given formula of the conjunctive nu-calculus (a suitable fragment of the mu-calculus) is undecidable.  Then, an equivalence between deterministic modal transition systems and a language-based formalism called modal specifications is developed.  Finally, the claim follows from a known equivalence between the conjunctive nu-calculus and modal specifications.

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Keywords
  • Petri net synthesis
  • conjunctive nu-Calculus
  • modal transition systems

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