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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© 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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