Relation algebras, matrices, and multi-valued decision diagrams

Authors:
Francis Atampore;Michael Winter
Affiliations:
Department of Computer Science, Brock University, St. Catharines, ON, Canada;Department of Computer Science, Brock University, St. Catharines, ON, Canada
Venue:
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Year:
2012

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Abstract

In this paper we want to further investigate the usage of matrices as a representation of relations within arbitrary heterogeneous relation algebras. First, we want to show that splittings do exist in matrix algebras assuming that the underlying algebra of the coefficients provides this operation. Second, we want to outline an implementation of matrix algebras using reduced ordered multi-valued decision diagrams. This implementation combines the efficiency of operations based on those data structures with the general matrix approach to arbitrary relation algebras.