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On Abstraction of Nets.

Desel, Jörg

In: Rozenberg, G.: Lecture Notes in Computer Science, Vol. 524; Advances in Petri Nets 1991, pages 78-92. Berlin, Germany: Springer-Verlag, 1991.

Abstract: The central idea of General net Theory is to emphasize morphisms between nets instead of studying single nets. The paper contributes to this theory and proposes a formalism for net transformations which is based on a subclass of surjective net morphisms, called abstractions. Each abstraction can be characterized by an equivalence relation on its elements. Feasible equivalence relations, which define abstractions, are characterized. They define quotient nets. Finally, it is shown that each abstraction can be decomposed into a folding and a simple contraction.

Keywords: abstraction (of nets); general net theory; surjective net morphism; net transformation; net equivalence; folding; contraction; coarsening (and) composition (of) nets.

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