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## A Proof of the Rank Theorem for Extended Free Choice Nets.

Desel, Jörg
In:
Jensen, K.: *Lecture Notes in Computer Science, Vol. 616; 13th International Conference on Application and Theory of Petri Nets 1992, Sheffield, UK*, pages 134-153.
Springer-Verlag,
June 1992.

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 well-formedness, 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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