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Semantics of Concurrent Computation pp 91–108Cite as

Notion de Dualite et de Symetrie dans les Reseaux de Petri

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 70))

Abstract

After having recalled some basic definitions and properties of the Petri nets, we synthesize some algebraic results, based upon a theorem of compatibility of linear inequalities systems (near of the Farkas lemma).

We find, as corollaries of equivalence theorems between algebraic propositions and Petri nets properties, two theorems synthesizing new results and scattered ones in the literature. Moreover, we refind a necessary condition for a Petri net to be live only based upon the structure of the graph, and also a symmetrical necessary condition for a Petri net to be bounded and live.

We recall, then, the leakage notion [10] and define the symmetrical notion of accumulator from where we derive a necessary condition for a Petri net to be bounded and live.

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Authors and Affiliations

  1. Institut de Programmation (E.R.A. — C.N.R.S. No 592), 4, Place Jussieu, 75230, PARIS CEDEX 05, FRANCE

    Gérard MEMMI

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  1. Gérard MEMMI
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Gilles Kahn

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© 1979 Springer-Verlag Berlin Heidelberg

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MEMMI, G. (1979). Notion de Dualite et de Symetrie dans les Reseaux de Petri. In: Kahn, G. (eds) Semantics of Concurrent Computation. Lecture Notes in Computer Science, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022465

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  • DOI: https://doi.org/10.1007/BFb0022465

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09511-8

  • Online ISBN: 978-3-540-35163-4

  • eBook Packages: Springer Book Archive

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