Synthesis of Nets with Step Firing Policies

Authors:
Philippe Darondeau;Maciej Koutny;Marta Pietkiewicz-Koutny;Alex Yakovlev
Affiliations:
IRISA, , Rennes Cedex, France F-35042;School of Computing Science, Newcastle University, Newcastle upon Tyne, United Kingdom NE1 7RU;School of Computing Science, Newcastle University, Newcastle upon Tyne, United Kingdom NE1 7RU;School of Electrical, Electronic and Computer Engineering, Newcastle University, Newcastle upon Tyne, United Kingdom NE1 7RU
Venue:
PETRI NETS '08 Proceedings of the 29th international conference on Applications and Theory of Petri Nets
Year:
2008

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Abstract

The unconstrained step semantics of Petri nets is impractical for simulating and modelling applications. In the past, this inadequacy has been alleviated by introducing various flavours of maximally concurrent semantics, as well as priority orders. In this paper, we introduce a general way of controlling step semantics of Petri nets through step firing policies that restrict the concurrent behaviour of Petri nets and so improve their execution and modelling features. In a nutshell, a step firing policy disables at each marking a subset of enabled steps which could otherwise be executed. We discuss various examples of step firing policies and then investigate the synthesis problem for Petri nets controlled by such policies. Using generalised regions of step transition systems, we provide an axiomatic characterisation of those transition systems which can be realised as reachability graphs of Petri nets controlled by a given step firing policy. We also provide a decision and synthesis algorithm for PT-nets and step firing policies based on linear rewards of steps, where fixing the reward of elementary transitions is part of the synthesis problem. The simplicity of the algorithm supports our claim that the proposed approach is practical.