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A proof of the Rank Theorem for extended free choice nets

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Application and Theory of Petri Nets 1992 (ICATPN 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 616))

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Abstract

A net is called well-formed if it can be marked with a live and bounded marking. The Rank Theorem characterises well-formed extended free choice nets, employing only the linear algebraic representation of a net. The paper presents a proof of the Rank Theorem which is based on the characterisation of liveness by deadlocks and traps and the coverability of well-formed extended free choice nets by S- and T-components. Consequences of the Rank Theorem include the Duality Theorem, a polynomial algorithm for deciding wellformedness, and simple proofs of other results concerning extended free choice nets. Moreover, the Rank Theorem implies a sufficient condition for liveness which applies to arbitrary nets.

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References

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Arcisstraße 21, D-8000, München 2

    Jörg Desel

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  1. Jörg Desel
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K. Jensen

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© 1992 Springer-Verlag Berlin Heidelberg

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Desel, J. (1992). A proof of the Rank Theorem for extended free choice nets. In: Jensen, K. (eds) Application and Theory of Petri Nets 1992. ICATPN 1992. Lecture Notes in Computer Science, vol 616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55676-1_8

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  • DOI: https://doi.org/10.1007/3-540-55676-1_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55676-3

  • Online ISBN: 978-3-540-47270-4

  • eBook Packages: Springer Book Archive

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