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The Kleene star is a unary operation on alphabets or sets of strings that creates the set of all finite concatenations of those strings.

Formal definitionEdit

Given any set A define

A_0=\{ \epsilon \} (where \epsilon is the empty string)
A_1=A
A_{i+1}=\{xy|w \in A_i \land y \in A \}

where xy is the concatenation of strings x and y.

Then Kleene star on A is defined as:

A^*=\bigcup_{i \in \mathbb{N}}V_i=V_1 \cup V_2 \ldots.

Kleene plusEdit

Kleene star without the empty string is kleene plus. Formally: V^+=V^* \setminus {\epsilon}

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