Synthesis of Weighted Marked Graphs from Constrained Labelled Transition Systems: A Geometric Approach
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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.
KeywordsWeighted 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.
- 11.Delosme, J.M., Hujsa, T., Munier-Kordon, A.: Polynomial sufficient conditions of well-behavedness for weighted join-free and choice-free systems. In: 13th International Conference on Application of Concurrency to System Design, pp. 90–99, July 2013Google Scholar
- 13.Barylska, K., Best, E., Erofeev, E., Mikulski, L., Piatkowski, M.: On binary words being Petri net solvable. In: Proceedings of the International Workshop on Algorithms & Theories for the Analysis of Event Data, ATAED 2015, Brussels, Belgium, pp. 1–15 (2015)Google Scholar
- 15.Erofeev, E., Barylska, K., Mikulski, L., Piatkowski, M.: Generating all minimal Petri net unsolvable binary words. In: Proceedings of the Prague Stringology Conference 2016, Prague, Czech Republic, pp. 33–46 (2016)Google Scholar
- 16.Erofeev, E., Wimmel, H.: Reachability graphs of two-transition Petri nets. In: Proceedings of the International Workshop on Algorithms & Theories for the Analysis of Event Data 2017, Zaragoza, Spain, pp. 39–54 (2017)Google Scholar
- 19.Hujsa, T.: Contribution to the study of weighted Petri nets. Ph.D. thesis, Pierre and Marie Curie University, Paris, France (2014)Google Scholar
- 20.Devillers, R., Erofeev, E., Hujsa, T.: Synthesis of weighted marked graphs from constrained labelled transition systems. In: Proceedings of the International Workshop on Algorithms & Theories for the Analysis of Event Data, Bratislava, Slovakia, pp. 75–90 (2018)Google Scholar
- 22.Devillers, R.: Products of transition systems and additions of Petri nets. In: Desel, J., Yakovlev, A. (eds.) Proceedings of 16th International Conference on Application of Concurrency to System Design (ACSD 2016), pp. 65–73 (2016)Google Scholar