Structured Operational Semantics for Graph Rewriting

Andrei Dorman
(LIPN – UMR 7030, Université Paris 13)
Tobias Heindel
(LIPN – UMR 7030, Université Paris 13)

Process calculi and graph transformation systems provide models of reactive systems with labelled transition semantics. While the semantics for process calculi is compositional, this is not the case for graph transformation systems, in general. Hence, the goal of this article is to obtain a compositional semantics for graph transformation system in analogy to the structural operational semantics (SOS) for Milner's Calculus of Communicating Systems (CCS).

The paper introduces an SOS style axiomatization of the standard labelled transition semantics for graph transformation systems. The first result is its equivalence with the so-called Borrowed Context technique. Unfortunately, the axiomatization is not compositional in the expected manner as no rule captures "internal" communication of sub-systems. The main result states that such a rule is derivable if the given graph transformation system enjoys a certain property, which we call "complementarity of actions". Archetypal examples of such systems are interaction nets. We also discuss problems that arise if "complementarity of actions" is violated.

In Alexandra Silva, Simon Bliudze, Roberto Bruni and Marco Carbone: Proceedings Fourth Interaction and Concurrency Experience (ICE 2011), Reykjavik, Iceland, 9th June 2011, Electronic Proceedings in Theoretical Computer Science 59, pp. 37–51.
Published: 31st July 2011.

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