Characterizing determinacy in Kleene algebras

Abstract Elements of Kleene algebras can be used, among other ways, as abstractions of the input–output semantics of nondeterministic programs or as models for the association of pointers with their target objects. One is interested in a notion of determinacy, in the first case, to distinguish deterministic programs and, in the second case, since it does not make sense for a pointer to point to two different objects. We discuss several candidate notions of determinacy and clarify their relationship. Some characterizations that are equivalent when the underlying Kleene algebra is an (abstract) relation algebra are not equivalent for general Kleene algebras.

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