General solution to a system of recursive equations on hypergraphs
A categorical framework has been described in [Ba89] to extend to systems of recursive equations on hypergraphs the classical results available for trees, such as the existence of an initial solution generalizing that of a least solution. As in the case of trees, the solution is not in general unique, but the situation is much more involved for hypergraphs. The aim of this paper is to present a classification of all the solutions of a system of recursive equations on hypergraphs.
Keywordshypergraphs hyperede rewriting systems of equations initial solution general solution
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- [Ba89]BAUDERON M., On some properties of infinite graphs, Proc. of the WG'88, Amsterdam, Lect. Not. Comp. Sci. 344, Springer Verlag, 1989, 54–73.Google Scholar
- [Ba90a]BAUDERON M., Infinite hypergraphs: I. Basic Properties, Report 90-20, University Bordeaux I, to appear in Theor. Comp. SciGoogle Scholar
- [Ba90b]BAUDERON M., Infinite hypergraphs: II. Systems of recursive equations on hypergraphs, revised version to appear in Theor. Comp. Sci.Google Scholar
- [Ca88]CAUCAL D., Pattern graphs, Research report 441, IRISA, 1988Google Scholar
- [Co88]COURCELLE B. Definable properties of equational graphs, to appear in Annals of Pure and Applied LogicGoogle Scholar
- [Co88c]COURCELLE B., Some applications of logic of universal algebra and of category theory to the theory of graph transformations, Tutorial, Bull. of the EATCS, 36, October 1988Google Scholar
- [Eh79]EHRIG H., Introduction to the algebraic theory of graphs, Lect. Not. Comp. Sci. 73 Springer 1977 1–69Google Scholar
- [HA89]HABEL A., Hyperedge replacement grammars and language, Thesis, Bremen 1989Google Scholar
- [HK87]HABEL A., KREOWSKY H-J., Some structural aspects of hypergraph languages generated by hyperedge replacement, Lect. Not. Comp. Sci; 247, 207–219 (1987) and May we introduce to you: hyperedge replacement, Lect Not. Comp. Sci.,291, 15–26, 1987Google Scholar
- [Mc71]McLANE S., Category for the working mathematician, Springer-Verlag 1971Google Scholar
- [SP82]SMYTH M.B., PLOTKIN G., The category theoretic solution to recursive domain equations, SIAM J. Comput. Vol. 11, No 4 (1982)Google Scholar