Representing hyper-graphs by regular languages

Abstract

A new compact representation of infinite graphs is investigated. Regular languages are used to represent labelled hyper-graphs which can be also multi-graphs. Our approach is similar to that used by A. Ehrenfeucht et al. for finite graphs since we use a regular prefix-free language as set of vertices, but it differs from that in the representation of the edges. In fact, we use a regular language for the edges instead of a finite loop-free graph. Our approach preserves the finite representation of the edges and of the corresponding labelling mapping and yields to a higher expressive power. As a matter of fact, our graph representation results to be more powerful than the equational graphs introduced by B. Courcelle. Moreover, the use of a regular prefix-free language to represent the vertices allows (fixed the language of the edges) to express a graph by a labelled tree. The advantage to represent graphs by trees is that properties of graphs can be verified by induction on the tree, often leading to efficient algorithms.

Partially supported by the M.U.R.S.T. in the framework of “Tecniche formali per la specifica, l'analisi, la verifica, la sintesi e la trasformazione di sistemi software” project.