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Separability in Persistent Petri Nets

100%

Best E. , Darondeau P.

2011

tom Vol. 113, nr 3/4

179-203

Separability in Petri nets means the property for a net k źN with an initial marking k źM to behave in the same way as k parallel instances of the same net N with an initial markingM, thus divided by k. We prove the separability of plain, bounded, reversible and persistent Petri nets, a class of nets that extends the well-known live and bounded marked graphs. We establish first a weak form of separability, already known to hold for marked graphs, in which every firing sequence of k ź N is simulated by a firing sequence of k parallel instances of N with an identical firing count. We establish on top of this a strong form of separability, in which every firing sequence of k ź N is simulated by an identical firing sequence of k parallel instances of N.

Making Petri Nets Safe and Free of Internal Transitions

80%

Best E. , Darondeau P. , Wimmel H.

2007

tom Vol. 80, nr 1-3

75-90

This paper discusses the following results: that bounded Petri nets can be transformed into pomset-equivalent safe nets; that bounded marked graphs can be transformed into step-language-equivalent safe marked graphs; that safe labelled marked graphs can be transformed into t-free safe labelled marked graphs; and that marked graphs can be separated. The paper also lists some open problems that have arisen in this context.