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
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