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.