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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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