Pre-synthesis of Petri nets based on prime cycles and distance paths

Abstract

This paper proposes a fail-fast pre-synthesis method supporting the synthesis of unlabelled Petri nets from labelled transition systems, while focusing on the class of choice-free systems. Such systems have applications, amongst others, in hardware design and in manufacturing. Necessary conditions which must be satisfied by any choice-freely Petri net synthesisable transition system will be identified. They include the prime cycle property and the distance path property, as well as various forms of determinism. Checking such properties before synthesis allows the early detection of non-synthesisable transition systems and the production of meaningful messages about the reasons of synthesis failure. Various interdependencies between these properties will be revealed. The prime cycle property and the distance path property will be shown to imply other ones. This allows pre-synthesis to be organised in an efficient way, because implied properties do not need to be checked if the properties they are implied by are already checked. • Reachability graphs of bounded choice free nets have many properties. • Relations between properties are explored. • Prime small loops and distance paths imply most needed properties. • This may be precious for a pre-synthesis phase.