Kleene Algebra with Domain (2003)
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@MISC{Desharnais03kleenealgebra,
author = {Jules Desharnais and Bernhard Möller and Georg Struth},
title = { Kleene Algebra with Domain},
year = {2003}
}
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Abstract
We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressibility of Kleene algebra, in particular for the specification and analysis of state transition systems. We develop the basic calculus, discuss some related theories and present the most important models of KAD. We demonstrate applicability by two examples: First, an algebraic reconstruction of Noethericity and well-foundedness. Second, an algebraic reconstruction of propositional Hoare logic.
