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String operations
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String operations : ウィキペディア英語版
String operations
In computer science, in the area of formal language theory, frequent use is made of a variety of string functions; however, the notation used is different from that used on computer programming, and some commonly used functions in the theoretical realm are rarely used when programming. This article defines some of these basic terms.
==Strings and languages==
A string is a finite sequence of characters.
The empty string is denoted by \varepsilon.
The concatenation of two string s and t is denoted by s \cdot t, or shorter by s t.
Concatenating with the empty string makes no difference: s \cdot \varepsilon = s = \varepsilon \cdot s.
Concatenation of strings is associative: s \cdot (t \cdot u) = (s \cdot t) \cdot u.
For example, (\langle b \rangle \cdot \langle l \rangle) \cdot (\varepsilon \cdot \langle ah \rangle) = \langle bl \rangle \cdot \langle ah \rangle = \langle blah \rangle.
A language is a finite or infinite set of strings.
Besides the usual set operations like union, intersection etc., concatenation can be applied to languages:
if both S and T are languages, their concatenation S \cdot T is defined as the set of concatenations of any string from S and any string from T, formally S \cdot T = \.
Again, the concatenation dot \cdot is often omitted for shortness.
The language \ consisting of just the empty string is to be distinguished from the empty language \.
Concatenating any language with the former doesn't make any change: S \cdot \ = S = \ \cdot S,
while concatenating with the latter always yields the empty language: S \cdot \ = \ = \ \cdot S.
Concatenation of languages is associative: S \cdot (T \cdot U) = (S \cdot T) \cdot U.
For example, abbreviating D = \, the set of all three-digit decimal numbers is obtained as D \cdot D \cdot D. The set of all decimal numbers of arbitrary length is an example for an infinite language.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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