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Graph Transformation with Time: Causality and Logical Clocks.

Gyapay, Szilvia; Heckel, Reiko; Varro, Daniel

In: Graph Transformation (ICGT 2002), Proceedings of the First International Conference, Barcelona, Spain, October 7-12, 2002, pages 120-134. Volume 2505 of Lecture Notes in Computer Science / A. Corradini, H. Ehrig, H.-J. Kreowski,G. Rozenberg (Eds.) --- Springer Verlag, October 2002.

Abstract: Following TER nets, an approach to the modelling of time in high-level Petri nets, we propose a model of time within (attributed) graph transformation systems where logical clocks are represented as distinguished node attributes. Corresponding axioms for the time model in TER nets are generalised to graph transformation systems and semantic variations are discussed. They are summarised by a general theorem ensuring the consistency of temporal order and casual dependencies.

The resulting notions of typed graph transformation with time specialise the algebraic double-pushout (DPO) approach to typed graph transformation. In particular, the concurrency theory of the DPO approach can be used in the transfer of the basic theory of TER nets.

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