Mixed Relations as Enriched Semiringal Categories

Abstract: A study of the classes of nite relations as enriched strict monoidal categories is presented in CaS91]. The relations there are interpreted as connections in owchart schemes, hence an \angelic" theory of relations is used. Finite relations may be used to model the connections between the components of data ow networks BeS98, BrS96], as well. The corresponding algebras are slightly di erent enriched strict monoidal categories modeling a \forward-demonic" theory of relations. In order to obtain a full model for parallel programs one needs to mix control and reactive parts, hence a richer theory of nite relations is needed. In this paper we (1) de ne a model of such mixed nite relations, (2) introduce enriched (weak) semiringal es as an abstract algebraic model for these relations, and (3) show that the initial model of the axiomatization (it always exists) is isomorphic to the de ned one of mixed relations. Hence the axioms gives a sound and complete axiomatization fo...

• Type: Journal
• Year: 2000
• Where: JUCS
• Authors: Radu Grosu, Dorel Lucanu, Gheorghe Stefanescu
• Keywords: JUCS 2000, Model, Nite Relations, Strict Monoidal Categories