Siphons, traps and high-level nets with infinite color domains
Commoner's Theorem establishes a relation between siphons, traps and liveness in free choice systems. Most proofs of this theorem do explicitly involve the finiteness of the net. Therefore we cannot apply the theorem directly to high level nets with infinite color domains.
We prove generalisations of both the “if” and the “only if” direction to the infinite case which unfortunately cannot be combined to an “iff” statement. We present examples which show that there are both live and non-live nets in the grey zone left by our generalisations. Our approach enlarges the application area of Commoner's theorem to infinite Petri nets, compared with an earlier generalisation to a class of free choice predicate event systems, but does not cover the other approach completely.
KeywordsTHEORY: Analysis and synthesis structure and behaviour of nets Higher-level net models
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