Polynomial algorithms for the synthesis of bounded nets

Abstract

The so-called synthesis problem for nets, which consists in deciding whether a given graph is isomorphic to the case graph of some net, and then constructing the net, has been solved in the litterature for various types of nets, ranging from elementary nets to Petri nets. The common principle for the synthesis is the idea of regions in graphs, representing possible extensions of places in nets. However, no practical algorithm has been defined so far for the synthesis. We give here exphcit algorithms solving in polynomial time the synthesis problem for bounded nets from regular languages or from finite automata. * This work was partly supported by the French P.R.c. ModUles et Preuves, by the H.C.M. Network Express, and by the H.C.M. fellowship granted to Luca Bernardinello, on leave from the University of Milan.

Process Discovery Using Integer Linear Programming

“…In this paper, we consider language-based region theory [8,13,17], of which [17] presents a nice overview. In [17], the authors show how for different classes of languages (step languages, regular languages and partial languages) a Petri net can be derived such that the resulting net is the smallest Petri net in which the words in the language are possible firing sequences.…”

“…each solution (x, y, c) of the inequation system can be regarded in the context of a Petri net, where the region corresponds to a feasible place with preset {t|t ∈ T, x(t) = 1} and postset {t|t ∈ T, y(t) = 1}, and initially marked with c tokens. Note that we do not assume arc-weights, where the authors of [8,11,13,17] do. However, in process modelling languages, such arc weights typically do not exist, hence we decided to ignore them.…”

Supervisory Control and High-level Petri nets

“…The aim of the theory of regions (Badouel et al, 1995) is to decide wether a given automaton is isomorphic to the reachability graph of a net, then constructing it. Ghaffari et al (Ghaffari et al, 2003) are the first who proposed an adaptation of this theory for the synthesis controller problem using Petri nets.…”

Process Model Discovery: A Method Based on Transition System Decomposition

“…The application of statebased region algorithms to process mining was studied in [6,9,21]. Algorithms based on regions of languages were presented in [7,14,18] and then applied to process mining [8,24]. State-based region algorithms and algorithms based on regions of languages map discovered regions into places of a target Petri net.…”