クリーネ shut parcel

The クリーネ shut parcel (くりーねへいほう British: Kleene closure) is a meeting of the lines (character string) of the symbol which repetition of a certain operation performs "generation" of to the letter in abstract language employing precise grammatical constructions and the theory of the automaton. In addition, an unary operator of this repetition is called クリーネスター (British: Kleene star).

V* refers to the application of the クリーネ shut parcel for meeting V. I am used in the regular expression that is the method that I introduced because Steven call クリーネ characterizes a certain automaton well.

1. When V is a set of the character string, I include empty character string ε, and V* is defined as the closed smallest meeting by character string connection operation. This meeting is a meeting of the character string that I connect character string more than 0 included in V and can make if I do a different form.
2. When V is the set of a symbol, the letter, V* is a set of every character string on V including the empty character string.

Example

The example of the クリーネ shut parcel applied to a set of the character string:

{"ab", "c"}* = {ε, "ab", "c", "abab", "abc", "cab", "cc", "ababab", "ababc", "abcab", "abcc", "cabab", "cabc", "ccab", "ccc", ...}

The example of the クリーネ shut parcel applied to the set of the letter:

{'a', 'b', 'c'}* = {ε, "a", "b", "c", "aa", "ab", "ac", "ba", "bb", "bc", ...}

Generalization

As for the クリーネ shut parcel, it is often made a binary operation on following monoid (M,.) that is meeting M and M meeting the following conditions the として public.

• （Shut parcel） For every a, b ∈ M, it is b ∈ M a
• (associative law) for every a, b, c ∈ M (a.b) It is c = a. (b.c)
• （Identity element） A certain ε ∈ M exists, and is every a ∈ M; a. It is a = a ε = ε

When V is a subset of M, V* includes ε (empty character string) and is the smallest meeting closed for operation. The V* itself becomes the monoid then and says with "monoid generated by V". In the set of the symbol because the set of every character string makes monoid (by the character string connection as the binary operation), this is generalization of the クリーネ shut parcel.

Allied item

• クリーネ algebra
• Expansion Bacchus Naur form
• Repetition lemma
• Regular expression

It is acquired by "https://ja.wikipedia.org/w/index.php?title= クリーネ 閉包 &oldid=62554610"

This article is taken from the Japanese Wikipedia クリーネ shut parcel

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