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A proof of the Rank Theorem for extended free choice nets

  • Jörg Desel
Submitted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 616)

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.

Keywords

free choice nets analysis, structure and behaviour of nets 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Jörg Desel
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenMünchen 2

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