Infinite hypergraphs I. Basic properties

Michael Bauderon
1991 Theoretical Computer Science  
Bauderon, M., Infinite hypergraphs I. Basic properties (Fundamental Study), Theoretical Computer Science 82 (1991) 177-214. Basic properties of the category of infinite directed hyperedge-iabeiied hypergraphs are studied. An algebraic structure is given which enables us to describe such hypergraphs by means of infinite expressions. It is then shown that two expressions define the same hypergraph if and only if they are congruent with respect to some rewriting system. These results will be used
more » ... n the second part of this paper to solve systems of recursive equations on hypergraphs and characterize their solutions. Rkume' On Ctudie ies propriCtb fondamentaies des hypergraphes infinis & hyperar&s Ctiquetees. Une structure aiggbrique est fournie qui permet de dCcrire de teis graphes g i'aide d'expressions infinies. On prouve que deux teiies expressions definissent ie m6me graphe si et seuiement si eiies sont congruentes moduio un certain syst$me de &criture. Ces risuitats seront utiiisis dans la seconde partie de cet article pour Ctudier certains systemes d'equations recursives sur ies hypergraphes et pour caracteriser ieurs solutions.
doi:10.1016/0304-3975(91)90222-n fatcat:pgk4emb4ufcjdklmioobuyjf7i