Kleene algebra
In mathematics and theoretical computer science, a Kleene algebra ( KLAY-nee; named after Stephen Cole Kleene) is a semiring that generalizes the theory of regular expressions: it consists of a set supporting union (addition), concatenation (multiplication), and Kleene star operations subject to certain algebraic laws. The addition is required to be idempotent ( x + x = x {\displaystyle x+x=x} for all x {\displaystyle x} ), and induces a partial order defined by x ≤ y {\displaystyle x\leq y} if x + y = y {\displaystyle x+y=y} .