Kleene algebra

In mathematics, a Kleene algebra (/ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is an idempotent (and thus partially ordered) semiring endowed with a closure operator. It generalizes the operations known from regular expressions.

This article is about the Kleene algebra with a closure operation—a generalization of regular expressions. For the Kleene algebra with involution—a generalization of Kleene's ternary logic—, see Kleene algebra (with involution).
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