Synthesis of weighted marked graphs from constrained labelled transition systems

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 su cient condition of WMG-solvability for an arbitrary number of letters. Finally, we show that this su cient condition is not necessary in the case of LTS forming a single circuit with five letters.SCOPUS: cp.pinfo:eu-repo/semantics/publishe

Synthesis of Weighted Marked Graphs from Constrained Labelled Transition Systems

International audienceRecent 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

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

22 pagesInternational audienceRecent 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

Zur Komplexität der Synthese von Petri-Netzen

Petri-Netz-Synthese fragt für ein reguläres Verhalten, das als Transitionssystem A gegeben ist, ob es ein Petri-Netz (einer bestimmten Klasse) gibt, das A implementiert. Diese Arbeit untersucht Varianten dieses Entscheidungsproblems für verschiedene Implementierungen und eine Vielzahl von Petri-Netz-Klassen aus Sicht der klassischen und der parametrisierten Komplexität. Ebenso wird die Komplexität der Modifikations-Techniken Neubeschriftung sowie Kanten-, Ereignis- und Zustandslöschung untersucht, die darauf abzielen, nicht-implememtierbare Transitionssysteme implementierbar zu machen.Petri net synthesis asks, for a regular behavior given as a transition system A, whether there exists a Petri net (of a particular class) that implements A. This work investigates variants of this decision problem for different implementations and a variety of Petri net classes from the point of view of classical and parameterized complexity. Also investigated is the complexity of the modification techniques of relabeling and edge, event, and state deletion, which aim to make non-implementable transition systems implementable