History of Kleene star

	Revision 11 . . December 20, 2001 11:48 pm by AxelBoldt
	Revision 10 . . (edit) August 21, 2001 6:07 pm by Jan Hidders

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Difference (from prior major revision) (no other diffs)

Changed: 2c2

# If V is a set of strings then its result is defined as the smallest superset of V that contains ε (the empty string) and is closed under the string concatenation operation. This set can also be described as the set of strings that can be made by concatenating zero or more strings from V.

# If V is a set of strings then V* is defined as the smallest superset of V that contains ε (the empty string) and is closed under the string concatenation operation. This set can also be described as the set of strings that can be made by concatenating zero or more strings from V.

Changed: 10c10

The Kleene star is often generalized for any Monoid (M, .), that is, a set M and binary operator '.' on M such that

The Kleene star is often generalized for any monoid (M, .), that is, a set M and binary operation '.' on M such that

Changed: 14c14

Then V* is defined as the smallest superset of V that contains e and is closed under the operation.

If V is a subset of M, then V* is defined as the smallest superset of V that contains e and is closed under the operation. V* is then itself a monoid, and is called the monoid generated by V. This is a generalization of the Kleene star discussed above since the set of all strings over some set of symbols forms a monoid (with string concatenation as binary operation).