Structured Operational Semantics for Graph Rewriting

TL;DR

This paper develops a structured operational semantics for graph rewriting systems, aiming for compositionality similar to process calculi, and introduces conditions under which such semantics are achievable.

Contribution

It introduces an SOS-style axiomatization for graph transformation systems and identifies a property called 'complementarity of actions' that enables compositional semantics.

Findings

Axiomatization equivalent to Borrowed Context technique

Identification of 'complementarity of actions' as key for compositionality

Discussion of issues when 'complementarity of actions' is absent

Abstract

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.