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Transition Systems of Elementary Net Systems with Localities

Lookup NU author(s): Professor Maciej KoutnyORCiD, Dr Marta Koutny



In this paper, we investigate transition systems of a class of Petri nets suitable for the modelling and behavioural analysis of globally asynchronous locally synchronous (GALS) systems. The considered model of Elementary Net Systems with Localities (ENL-systems) is basically that of Elementary Net Systems (EN-systems) equipped with an explicit notion of locality. Each locality identifies a distinct set of events which may only be executed synchronously, i.e., in a maximally concurrent manner. For this reason, the overall behaviour of an ENL-system cannot be represented by an interleaved transition system, with arcs being labelled by single events, but rather by a suitable notion of a step transition system, with arcs being labelled by sets of events executed concurrently. We completely characterise transition systems which can be generated by Elementary Net Systems with Localities under their intended concurrency semantics. In developing a suitable characterisation, we follow the standard approach in which key relationships between a Petri net and its transition system are established via the the regions of the latter defined as specific sets of states of the transition system. We argue that this definition is insufficient for the class of transition systems of ENL-systems, and then augment the standard notion of a region with some additional information, leading to the notion of a region with explicit input and output events (or io-region). We define, and show consistency of, two behaviour preserving translations between ENL-systems and their transition systems. As a result, we provide a solution to the synthesis problem of Elementary Net Systems with Localities, which consists in constructing an ENL-system for a given transition system in such a way that the transition system of the former is isomorphic to the latter.

Publication metadata

Author(s): Koutny M, Pietkiewicz-Koutny M

Publication type: Report

Publication status: Published

Series Title: School of Computing Science Technical Report Series

Year: 2006

Pages: 19

Print publication date: 01/02/2006

Source Publication Date: February 2006

Report Number: 948

Institution: School of Computing Science, University of Newcastle upon Tyne

Place Published: Newcastle upon Tyne