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 Kleene star (Definition)

If is an alphabet (a set of symbols), then the Kleene star of , denoted , is the set of all strings of finite length consisting of symbols in , including the empty string .

If is a set of strings, then the Kleene star of , denoted , is the smallest superset of that contains and is closed under the string concatenation operation. That is, is the set of all strings that can be generated by concatenating zero or more strings in .

The definition of Kleene star can be generalized so that it operates on any monoid , where is a binary operation on the set . If is the identity element of and is a subset of , then is the smallest superset of that contains and is closed under .

### Examples

"Kleene star" is owned by Logan.
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See Also: alphabet, string, regular expression, Kleene algebra, language, convolution, weight (strings), weight enumerator

Cross-references: subset, identity element, binary operation, monoid, generated by, operation, closed under, contains, superset, empty string, length, finite, strings, alphabet
There are 4 references to this entry.

This is version 2 of Kleene star, born on 2002-02-24, modified 2002-05-03.
Object id is 2584, canonical name is KleeneStar.
Accessed 3897 times total.

Classification:
 AMS MSC: 68Q70 (Computer science :: Theory of computing :: Algebraic theory of languages and automata) 20M35 (Group theory and generalizations :: Semigroups :: Semigroups in automata theory, linguistics, etc.)

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