Synthesis of Weighted Marked Graphs from Constrained Labelled Transition Systems: A Geometric Approach

Part of the Lecture Notes in Computer Science book series (LNCS, volume 11790)


Recent studies investigated the problems of analysing Petri nets and synthesising them from labelled transition systems (LTS) with two labels (transitions) only. In this paper, we extend these works by providing new conditions for the synthesis of 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.

Some of these new conditions do not restrict the number of labels; the other ones consider up to 3 labels. Additional constraints are investigated: when the LTS is either finite or infinite, and either cyclic or acyclic. We show that one of these conditions, developed for 3 labels, does not extend to 4 nor to 5 labels. Also, we tackle geometrically the WMG-solvability of finite, acyclic LTS with any number of labels.


Weighted Petri net Marked graph Synthesis Labelled transition system Cycles Cyclic words Circular solvability Theory of regions Geometric interpretation 



We would like to thank the anonymous referees for their involvement and useful suggestions.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Département d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Department of Computing ScienceCarl von Ossietzky Universität OldenburgOldenburgGermany
  3. 3.LAAS-CNRS, Université de Toulouse, CNRSToulouseFrance

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