Kleene algebra with domain

Details Kleene algebra with domain Kleene algebra with domain

2003-10-28

arxiv.org/abs/cs/0310054v1

Computer Science

Logic in Computer Science

40 pages

Scientific paper

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 expressiveness 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.

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