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Graph grammars as context-dependent rewriting systems: A partial ordering semantics

  • Ugo Montanari
  • Francesca Rossi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 581)

Abstract

Context-dependent rewriting systems allow a higher degree of concurrency w.r.t. context-independent ones, since rewriting rules which apply in intersecting contexts and rewrite different items may be applied concurrently, while this cannot happen with a context-independent specification of the same rules. Context-dependent systems can also be seen as a natural generalization of read/write systems, where several readers of the same items may proceed in parallel. However, all the partial ordering semantics which have been given in the past apply, as far as we know, to context-independent systems. In this paper, instead, we investigate the possibility of giving a partial ordering semantics to graph grammars, which can be seen as elegant and general context-dependent rewriting systems. We accomplish that by associating a deterministic occurrence Petri net to each graph derivation. From such a net, then, a partial ordering relating the applied productions, and expressing the causal dependencies among them, can be obtained. The set of all such partial orderings is then the semantics of the given grammar. We also compare our approach with the classical one for concurrency in graph grammars, and we show that, given a derivation, they generate the same dependencies, although our approach is more abstract than the classical one.

Keywords

Inference Rule Graph Production Graph Grammar Production Application Causal Dependency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Ugo Montanari
    • 1
  • Francesca Rossi
    • 1
  1. 1.Computer Science DepartmentUniversity of PisaPisaItaly

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