Affiliations: Centre de recherche INRIA, Rennes-Bretagne Atlantique,
campus de Beaulieu, F-35042 Rennes Cedex, France. E-mail:
[email protected] | School of Computing Science, Newcastle University,
Newcastle upon Tyne, NE1 7RU, United Kingdom. E-mail:
{maciej.koutny,marta.koutny}@newcastle.ac.uk | School of Electrical, Electronic and Computer
Engineering, Newcastle University, Newcastle upon Tyne, NE1 7RU, United
Kingdom. E-mail: [email protected]
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 two different
decision and synthesis algorithms for PT-nets and step firing policies based on
linear rewards of steps, where the reward for firing a single transition is
either fixed or it depends on the current net marking. The simplicity of the
algorithms supports our claim that the proposed approach is practical.
Keywords: Petri nets, step firing policy, step transition system, regions, synthesis problem
