Kleene Star - Definition and Notation

Definition and Notation

Given a set

define

the null string "" and

define recursively the set

where

If V is a formal language, then V_i, the i-th power of the set V, is a shorthand for the concatenation of set V with itself i times. That is, V_i can be understood to be the set of all strings that can be represented as the concatenation of i strings in .

The definition of Kleene star on V is