Target-oriented Petri Net Synthesis

Abstract

When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

A New Property of Choice-Free Petri Net Systems

“…Like for the classic choice-free synthesis problem (as well as many other targeted synthesis problems [6]), the synthesis procedure may be separated into a pre-synthesis and a proper synthesis. The pre-synthesis allows to quickly check properties of the structure of the reachability graph(s), from the structure of the class of nets aimed for.…”

Synthesis of Inhibitor-Reset Petri Nets: Algorithmic and Complexity Issues

“…In particular, if the behavior of a system is specified by a finite labeled transition system (LTS for short), more or less efficient algorithms have been developed to build a bounded weighted Petri net with a reachability graph isomorphic to (or close to) the given LTS [3,23]. It is also possible to target some subclasses of Petri nets [8], in particular choice-free nets and some of their specializations [9,10,7,15] which present interesting features.…”

Synthesis of (Choice-Free) Reset Nets

“…In particular, if the behaviour of a system is specified by a finite labelled transition system (LTS for short), more or less efficient algorithms have been developed to build a bounded weighted Petri net with a reachability graph isomorphic to (or close to) the given LTS [2,19]. It is also possible to target some subclasses of Petri nets [6], in particular choice-free nets and some of their specialisations [7,8,4,13] which present interesting features.…”