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*∧−*x*≤*y*∨−*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

### Other articles related to "kleene algebra, kleene algebras, kleene, algebras":

**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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