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Concurrency and loose semantics of open graph transformation systems

Published online by Cambridge University Press:  16 September 2002

REIKO HECKEL ,
MERCÉ LLABRÉS ,
HARTMUT EHRIG  and
FERNANDO OREJAS
REIKO HECKEL
Affiliation:
University of Paderborn, Germany Email: reiko@uni-paderborn.de
MERCÉ LLABRÉS
Affiliation:
University of the Balearic Islands, Palma de Mallorca, Spain Email: merce@ipc4.uib.es
HARTMUT EHRIG
Affiliation:
Technical University of Berlin, Germany Email: ehrig@cs.tu-berlin.de
FERNANDO OREJAS
Affiliation:
Technical University of Catalonia, Spain Email: orejas@lsi.upc.es
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Abstract

Graph transitions represent an extension of the DPO approach to graph transformation for the specification of reactive systems. In this paper, we develop the theory of concurrency for graph transitions. In particular, we prove a local Church–Rosser theorem and define a notion of shift-equivalence that allows us to represent both intra-concurrency (within the specified subsystem) and inter-concurrency (between subsystem and environment). Via an implementation of transitions in terms of DPO transformations with context rules, a second, more restrictive notion of equivalence is defined that captures, in addition, the extra-concurrency (between operations of the environment). As a running example and motivation, we show how the concepts of this paper provide a formal model for distributed information systems.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 12 , Issue 4 , August 2002 , pp. 349 - 376
Copyright
2002 Cambridge University Press

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Footnotes

This paper is a complete and revised version of a lecture given at the workshop on Theory and Applications of Graph Transformations (GRATRA 2000), which was a satellite event of ETAPS 2000 in Berlin, March 2000.