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

TL;DR

This paper introduces new geometric conditions for synthesizing Weighted Marked Graphs from labelled transition systems, extending prior work to systems with multiple labels and various structural constraints.

Contribution

It provides novel synthesis conditions for Weighted Marked Graphs from labelled transition systems, including cases with up to three labels and geometric analysis for arbitrary labels.

Findings

New conditions for WMG synthesis from LTS with up to 3 labels.

Geometric approach to WMG solvability for finite, acyclic LTS.

Identification of limitations when extending conditions to more than 3 labels.

Abstract

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.