Definitions and comparisons of local computations on graphs

Abstract

We are interested in models to encode and to prove decentralized and distributed computations on graphs or networks. In this paper, we define and compare six models of graph rewriting systems. These systems do not change the underlying structure of the graph on which they work, but only the labelling of its components (edges or vertices). Each rewriting step is fully determinated by the knowledge of a fixed size subgraph, the local context of the rewritten occurrence. The studied families are based on the rewriting of partial or induced subgraphs and we use two kinds of mechanisms to locally control the applicability of rules: a priority relation on the set of rules or a set of forbidden contexts associated with each rule. We show that these two basic (i.e. without local control) families of graph rewriting systems are distinct, but whenever we consider the local controls of the rewriting, the four so-obtained families are equivalent.

With the support of the PRO Mathématiques et Informatique and the European Basic Research Action ESPRIT No 3166 ASMICS.