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On Abstractions of Nets.

Desel, Jörg

2/90 B: TUM--Report; SFB-Bericht No. 342, pages 1-22 pp.. München, Germany: Technische Universiät, Institut für Informatik, Sonderforschungsbereich ``Methoden und Werkzeuge für die Nutzung paralleler Rechnerarchitekturen'', April 1990.

Abstract: The central idea of Genearl Net Theory is to emphasise morphisms between nets. The paper contributes to this theory and proposes a formalism for net transformations based on abstractions which are special surjective net morphisms. Abstractions can be characterised by an equivalence relation on the elements of the net. Feasible equivalence relations, which define abstractions, are characterised. It is clarified to what extent the notion and properties of quotient sets can carried over to quotient nets. It is shown that each abstraction can be decomposed into foldings (a subclass of abstractions) and loop contractions (simple local transformations).

Keywords: decomposition (of) net abstraction; net morphism; genearl net theory; quotient net; net folding; loop contraction.

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