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International Conference on Application and Theory of Petri Nets

ICATPN 1997: Application and Theory of Petri Nets 1997 pp 271–289Cite as

Siphons, traps and high-level nets with infinite color domains

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1248))

Abstract

Commoner's Theorem establishes a relation between siphons, traps and liveness in free choice systems. Most proofs of this theorem do explicitly involve the finiteness of the net. Therefore we cannot apply the theorem directly to high level nets with infinite color domains.

We prove generalisations of both the “if” and the “only if” direction to the infinite case which unfortunately cannot be combined to an “iff” statement. We present examples which show that there are both live and non-live nets in the grey zone left by our generalisations. Our approach enlarges the application area of Commoner's theorem to infinite Petri nets, compared with an earlier generalisation to a class of free choice predicate event systems, but does not cover the other approach completely.

Supported by a scholarship of German Academic Exchange Service (DAAD)

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Author information

Authors and Affiliations

  1. '96:Digital Systems Laboratory Department of Computer Science, Helsinki University of Technology, 02150, Espoo, Finland

    Karsten Schmidt

  2. '97: Institute of Algebra, University of Technology, 01062, Dresden, Germany

    Karsten Schmidt

Authors
  1. Karsten Schmidt
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Editor information

Pierre Azéma Gianfranco Balbo

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© 1997 Springer-Verlag Berlin Heidelberg

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Schmidt, K. (1997). Siphons, traps and high-level nets with infinite color domains. In: Azéma, P., Balbo, G. (eds) Application and Theory of Petri Nets 1997. ICATPN 1997. Lecture Notes in Computer Science, vol 1248. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63139-9_41

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  • DOI: https://doi.org/10.1007/3-540-63139-9_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63139-2

  • Online ISBN: 978-3-540-69187-7

  • eBook Packages: Springer Book Archive

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