Kleene star

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In formal language theory, the Kleene star (or Kleene operator or Kleene closure) refers to two related unary operations, that can be applied either to an alphabet of symbols or to a formal language, a set of strings (finite sequences of symbols). The Kleene star operator on an alphabet V generates the set V* of all finite-length strings over V, that is, finite sequences whose elements belong to V; in mathematics, it is more commonly known as the free monoid construction. The Kleene star operator on a language L generates another language L*, the set of all strings that can be obtained as a concatenation of zero or more members of L. In both cases, repetitions are allowed. The Kleene star operators are named after American mathematician Stephen Cole Kleene, who first introduced and widely used it to characterize automata for regular expressions.

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