Rectangles, fringes, and inverses

Authors:
Gunther Schmidt
Affiliations:
Institute for Software Technology, Department of Computing Science, Universität der Bundeswehr München, Neubiberg, Germany
Venue:
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Year:
2008

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Abstract

Relational composition is an associative operation; therefore semigroup considerations often help in relational algebra. We study here some less known such effects and relate them with maximal rectangles inside a relation, i.e., with the basis of concept lattice considerations. The set of points contained in precisely one maximal rectangle makes up the fringe. We show that the converse of the fringe sometimes acts as a generalized inverse of a relation. Regular relations have a generalized inverse. They may be characterized by an algebraic condition.