4 research outputs found
Products in categories of relations
AbstractThe relational product construction is often consider as an abstract version of cartesian products. The existence of those products is strongly connected with the representability of that category. In this paper we investigate a canonical weakening of the notion of a relational product. Unlike the strong version, any (small) category of relations can be embedded into a suitable category providing all weak relational products. Furthermore, we provide several examples, and we study the categorical properties of the new construction
Weak n-Ary Relational Products in Allegories
Allegories are enriched categories generalizing a category of sets and binary relations. Accordingly, relational products in an allegory can be viewed as a generalization of Cartesian products. There are several definitions of relational products currently in the literature. Interestingly, definitions for binary products do not generalize easily to n-ary ones. In this paper, we provide a new definition of an n-ary relational product, and we examine its properties.We would like to thank the reviewers for their helpful suggestions
Relation-algebraic modeling and solution of chessboard independence and domination problems
AbstractWe describe a simple computing technique for solving independence and domination problems on rectangular chessboards. It rests upon relational modeling and uses the BDD-based specific purpose computer algebra system RelView for the evaluation of the relation-algebraic expressions that specify the problems’ solutions and the visualization of the computed results. The technique described in the paper is very flexible and especially appropriate for experimentation. It can easily be applied to other chessboard problems