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memo

Kleene Star

Kleene Star

Kleene star or Kleene Closure.

Given a set $V$.

\[\begin{eqnarray} V^{0} & := & \{ \epsilon \} \nonumber \\ V^{1} & := & V \nonumber \\ V^{i+1} & := & \{wv \mid w \in V^{i}, v \in V\} \end{eqnarray}\]

Kleene star of $V$ is

\[V^{*} := \bigcup_{i \ge 0} V^{i} .\]

Reference