Graph relabelling systems have been introduced as a suitable model for expressing and studying distributed algorithms on a network of communicating processors. We recall the basic ideas underlying that model and we present the main questions that have been considered and the main results that have been obtained in that framework.

. In this paper we give a formalization of the problem of locally detecting the global termination of distributed algorithms on graphs. We introduce the notion of quasi k\Gammacoverings. Using (quasi) k\Gammacoverings, we present methods for showing that it is not possible to detect locally the global termination of local computations in certain families of graphs. These methods also allow to show that some knowledge, e.g. the size of the graph, is necessary in order to solve certain problems in a distributed way. Keywords: local detection of termination, local computations, k\Gammacovering, quasi k\Gammacovering. 1 Introduction Local computations on graphs, as given by graph rewriting systems (with priorities and/or forbidden contexts) are a powerful model for local computations which can be executed in parallel. Rewriting systems provide a general tool for encoding distributed algorithms and for proving their correctness. This paper is concerned with the existence of rewriting syst...