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Theory of Regions.

Badouel, Eric; Darondeau, Philippe

In: Reisig, W.; Rozenberg, G.: Lecture Notes in Computer Science, Vol. 1491: Lectures on Petri Nets I: Basic Models, pages 529-586. Springer-Verlag, 1998.

Abstract: The synthesis problem for nets consists in deciding whether a given graph is isomorphic to the marking graph of some net and then constructing it. This problem has been solved in the literature for various types of nets ranging from elementary nets to Petri nets. The general principle for the synthesis is to inspect regions of graphs representing extensions of places of the likely generating nets. We follow in this survey the gradual development of the theory of regions from its foundation by Ehrenfeucht and Rozenberg, with a particular insistence on the abstract meaning of the theory, which is a general product decomposition of graphs into atomic components determined by a parameter called a type of nets, and on the derivation of efficient algorithms for net synthesis based on linear algebra.

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