Synthesis of Weighted Marked Graphs from Constrained Labelled Transition Systems

Raymond Devillers (1) , Evgeny Erofeev (2) , Thomas Hujsa (3)

1 Département d'Informatique
2 OFFIS - Carl Von Ossietzky Universität Oldenburg = Carl von Ossietzky University of Oldenburg
3 DTIS, ONERA, Université de Toulouse [Toulouse]

Recent studies investigated the problems of analyzing Petri nets and synthesizing them from labelled transition systems (LTS) with two letters (transitions) only. In this paper, we extend these works by providing new characterizations for the synthesis of two-and three-letter Weighted Marked Graphs (WMGs), a well-known and useful class of weighted Petri nets in which each place has at most one input and one output. In this study, we focus mainly on LTS forming a single circuit. Also, we develop a sufficient condition of WMG-solvability for an arbitrary number of letters. Finally, we show that this sufficient condition is not necessary in the case of LTS forming a single circuit with five letters.

Mots clés: Weighted Petri net; marked graph; synthesis; labelled transition system; cycles; cyclic words; circular solvability

Domaines: Systèmes embarqués; Calcul parallèle, distribué et partagé [cs.DC]

Raymond Devillers, Evgeny Erofeev, Thomas Hujsa. Synthesis of Weighted Marked Graphs from Constrained Labelled Transition Systems. ATAED@Petri Nets/ACSD 2018, Jun 2018, Bratislava, Slovakia. ⟨hal-02127780⟩