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Time Processes for Time Petri Nets

Tuomas Aura

Helsinki University of Technology, FIN-02015 HUT, Finland

## Abstract

Time Petri nets are Petri nets extended with a notion of time, where
the occurrence time of a transition is constrained by a static
interval. The objective of this work is to give time Petri nets a
partial order semantics based on the nonsequential processes semantics
for untimed net systems. A time process of a time Petri net is defined
as a traditionally constructed causal process that has a valid
timing. This means that the events of the process are labeled with
occurrence times which must satisfy specific validness criteria. These
criteria are obtained by analyzing how the timing constraints interact
with the causal ordering of the events in the net. An efficient
algorithm for checking then validness of a given timing is
sketched. Interleavings of the time processes are defined as
linearizations of the causal partial order of events where also the
temporal ordering of events is preserved. The relationship between the
firing schedules of a time Petri net and the interleavings of the time
processes of the net is shown to be bijective. Also, a sufficient
condition is given for when the invalidity of timings for a process
can be inferred from an initial subprocess. An alternative
characterization for the validness of timings then results in an
algorithm for constructing the set of all valid timings for a
process. This set of all valid timings is presented as sets of
alternative linear constraints from which the existence of a valid
timing can be decided.

Full paper in Postscript

@InProceedings{AurLil97,
author = {Tuomas Aura and Johan Lilius},
title = {Time processes of time Petri nets},
booktitle = {Proc.\ 18th Int.\ Conf.\ on Application and
Theory of Petri nets},
volume = 1248,
series = {LNCS},
pages = "136--155",
year = 1997,
publisher = {Springer Verlag},
month = jun
}