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1

Separability in Persistent Petri Nets

Best E., Darondeau P.

Fundamenta Informaticae

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2011

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Vol. 113, nr 3/4

179-203

EN

Separability in Petri nets means the property for a net k źN with an initial marking k źM to behave in the same way as k parallel instances of the same net N with an initial markingM, thus divided by k. We prove the separability of plain, bounded, reversible and persistent Petri nets, a class of nets that extends the well-known live and bounded marked graphs. We establish first a weak form of separability, already known to hold for marked graphs, in which every firing sequence of k ź N is simulated by a firing sequence of k parallel instances of N with an identical firing count. We establish on top of this a strong form of separability, in which every firing sequence of k ź N is simulated by an identical firing sequence of k parallel instances of N.

2

Synthesis of Nets with Step Firing Policies

Darondeau P., Koutny M., Pietkiewicz-Koutny M., Yakovlev A.

Fundamenta Informaticae

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2009

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Vol. 94, nr 3/4

275-303

EN

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.

3

Making Petri Nets Safe and Free of Internal Transitions

Best E., Darondeau P., Wimmel H.

Fundamenta Informaticae

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2007

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Vol. 80, nr 1-3

75-90

EN

This paper discusses the following results: that bounded Petri nets can be transformed into pomset-equivalent safe nets; that bounded marked graphs can be transformed into step-language-equivalent safe marked graphs; that safe labelled marked graphs can be transformed into t-free safe labelled marked graphs; and that marked graphs can be separated. The paper also lists some open problems that have arisen in this context.

4

Transition systems without transitions

Borzyszkowski A. M., Darondeau P.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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2003

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Nr 964

1-7

EN

We study the problem of embedding partial 2-structures into set 2-structures such that the target substructure is full and forward closed and it is minimal w.r.t. these properties.

PL

Badamy problem takiego zanurzenia częściowej 2-struktury w 2-strukturę zbiorową, by docelowa 2-struktura była pełna, domknięta w przód i minimalna względem tych własności.