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Full Axiomatisation of Timed Processes of Interval-Timed Petri Nets

Pelz E.

Fundamenta Informaticae

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2018

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Vol. 157, nr 4

427--442

EN

In this paper we use partial order semantics to express the truly concurrent behaviour of Interval-Timed Petri nets (ITPNs) in their most general setting, i.e. with autoconcurrency and zero duration, as studied with its standard maximal step semantics in [1]. First we introduce the notion of timed processes for ITPNs inductively. Then we investigate if the equivalence of inductive and axiomatic process semantics - true for classical Petri nets - could hold for ITPNs too. We will see that the notions of independence and immediate firing obligation seem to be antagonistic ones, and that local axioms, adequate to define processes of classical Petri nets, are not sufficient to caracterize timed processes of ITPNs. We propose several original “global” axioms which reveal to be an effective solution. Thus we yield finally a full axiomatic definition of timed processes for ITPNs.

2

A Holistic State Equation for Timed Petri Nets

Werner M., Popova-Zeugmann L., Haustein M., Pelz E.

Fundamenta Informaticae

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2014

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Vol. 133, nr 2/3

305--322

EN

In this paper we investigate Timed Petri nets (TPN) with fixed, possibly zero, durations and maximal step semantics. We define a new state representationwhere a state is a pair of a marking for the places and a marking for the transitions (a matrix of clocks). For this representation of states we provide an algebraic state equation. Such a state equation lets us prove a sufficient condition for the non-reachability of a state in a TPN. This application of the state equation is subsequently illustrated by an example.

3

Algebraical Characterisation of Interval-Timed Petri Nets with Discrete Delays

Popova-Zeugmann L., Pelz E.

Fundamenta Informaticae

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2012

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Vol. 120, nr 3/4

341-357

EN

In this paper we consider Interval-Timed Petri nets (ITPN) which are an extension of Timed Petri nets. They are considered to behave with discrete delays. The class of ITPNs is Turing complete and therefore the reachability of an arbitrary marking in such a net is not decidable. We introduce a time dependent state equation for a firing sequence of ITPNs, which is analogous to the state equation for a firing sequence in standard Petri nets and we prove its correctness using linear algebra. Our result is original and delivers both a necessary condition for reachability and a sufficient condition for non-reachability of an arbitrary marking in an ITPN.