Kleene Algebra

In mathematics, a Kleene algebra ( /ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is either of two different things:

  • A bounded distributive lattice with an involution satisfying De Morgan's laws (i.e. a De Morgan algebra), additionally satisfying the inequality x∧−xy∨−y. Kleene (and De Morgan) algebras are subclasses of Ockham algebras. The simplest Kleene algebra of this kind is Kleene's three-valued logic K3. (This is analogous to Boolean logic being the simplest Boolean algebra.)
  • An algebraic structure that generalizes the operations known from regular expressions. The remainder of this article deals with this notion of Kleene algebra.

Read more about Kleene Algebra:  Definition, Examples, Properties, History

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Kleene Algebra - History
... Kleene algebras were not defined by Kleene he introduced regular expressions and asked for a complete set of axioms, which would allow derivation of all equations among regular expressions ... first studied by John Horton Conway under the name of regular algebras ... The axioms of Kleene algebras solve this problem, as was first shown by Dexter Kozen ...

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