Visualization of Distributed Algorithms Based on Graph Relabelling Systems1 1This work has been supported by the European TMR research network GETGRATS, and by the “Conseil Régional d' Aquitane”.

AbstractIn this paper, we present a uniform approach to simulate and visualize distributed algorithms encoded by graph relabelling systems. In particular, we use the distributed applications of local relabelling rules to automatically display the execution of the whole distributed algorithm. We have developed a Java prototype tool for implementing and visualizing distributed algorithms. We illustrate the different aspects of our framework using various distributed algorithms including election and spanning trees

Characterizing Compressibility of Disjoint Subgraphs with NLC Grammars

We consider compression of a given set S of isomorphic and disjoint subgraphs of a graph G using node label controlled (NLC) graph grammars. Given S and G, we characterize whether or not there exists a NLC graph grammar consisting of exactly one rule such that (1) each of the subgraphs S in G are compressed (i.e., replaced by a nonterminal) in the (unique) initial graph I , and (2) the set of generated terminal graphs is the singleton {G}.acceptance rate: 39%status: publishe

Representing First-Order Logic Using Graphs

Abstract. We show how edge-labelled graphs can be used to represent first-order logic formulae. This gives rise to recursively nested structures, in which each level of nesting corresponds to the negation of a set of existentials. The model is a direct generalisation of the negative application conditions used in graph rewriting, which count a single level of nesting and are thereby shown to correspond to the fragment ∃¬∃ of first-order logic. Vice versa, this generalisation may be used to strengthen the notion of application conditions. We then proceed to show how these nested models may be flattened to (sets of) plain graphs, by allowing some structure on the labels. The resulting formulae-as-graphs may form the basis of a unification of the theories of graph transformation and predicate transformation

Visualisation of distributed algorithms based on graph relabelling systems

In this paper, we present a uniform approach to simulate and visualize distributed algorithms encoded by graph relabelling systems. In particular, we use the distributed applications of local relabelling rules to automatically display the execution of the whole distributed algorithm. We have developed a Java prototype tool for implementing and visualizing distributed algorithms. We illustrate the different aspects of our framework using various distributed algorithms including election and spanning trees.from: Electronic Notes in Theoretical Computer Science Vol.50 No.