How to calculate symmetries of Petri nets |
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Authors: | Karsten Schmidt |
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Affiliation: | Institut für Informatik, Humboldt-Universit?t zu Berlin, D-10099 Berlin, Germany (e-mail: kschmidt@informatik.hu-berlin.de, Fax: (+49) (30) 2093 3081), DE
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Abstract: | Symmetric net structure yields symmetric net behaviour. Thus, knowing the symmetries of a net, redundant calculations can
be skipped. We present a framework for the calculation of symmetries for several net classes including place/transition nets,
timed nets, stochastic nets, self–modifying nets, nets with inhibitor arcs, and many others. Our approach allows the specification
of different symmetry groups. Additionally it provides facilities either to calculate symmetries on demand while running the
actual analysis algorithm, or to calculate them in advance. For the latter case we define and calculate a ground set of symmetries. Such a set has polynomial size and is sufficient for an efficient implementation of the for all symmetries loop and the partition of net elements into equivalence classes. These two constructions are the usual way to integrate symmetries
into an analysis algorithm.
Received 7 July 1997 / 10 August 1999 |
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