“concatenation”的概念、定义、翻译、参考文献-科学参考

concatenation

Mathematics

Concatenation is a binary operation on words, which places one word after another. For example, given the binary words w₁ = 10 and w₂ = 1101, then their concatenation is w₁ w₂ = 101101. Concatenation is the group operation for free groups and groups defined by a presentation.

Computer

The operation of joining two strings to form a longer string. The concatenation of the strings
$u = a_{1}, \dots, a_{m} and v = b_{1}, \dots, b_{n}$
is the following string of length m + n:
$a_{1}, \dots, a_{m} b_{1}, \dots, b_{n}$
Common notations for referring to it include uv and u<>v, but others are also used.
The term concatenation is also generalized to an operation on sets of strings (i.e. formal languages). Let K and L be two sets of strings. Then they can be combined into the following set by concatenating strings from K with strings from L in all possible ways:
${u v | u \in K, v \in L}$
This set is usually written KL. The phrase language concatenation is sometimes used to distinguish this from simple concatenation of strings. Both string concatenation and language concatenation give rise to monoids, the identity elements being ∧‎ and {∧‎} respectively (where ∧‎ is the empty string).

单词	concatenation
释义	concatenation Mathematics Concatenation is a binary operation on words, which places one word after another. For example, given the binary words w₁ = 10 and w₂ = 1101, then their concatenation is w₁ w₂ = 101101. Concatenation is the group operation for free groups and groups defined by a presentation. Computer The operation of joining two strings to form a longer string. The concatenation of the strings $u = a_{1}, \dots, a_{m} and v = b_{1}, \dots, b_{n}$ is the following string of length m + n: $a_{1}, \dots, a_{m} b_{1}, \dots, b_{n}$ Common notations for referring to it include uv and u<>v, but others are also used. The term concatenation is also generalized to an operation on sets of strings (i.e. formal languages). Let K and L be two sets of strings. Then they can be combined into the following set by concatenating strings from K with strings from L in all possible ways: ${u v \| u \in K, v \in L}$ This set is usually written KL. The phrase language concatenation is sometimes used to distinguish this from simple concatenation of strings. Both string concatenation and language concatenation give rise to monoids, the identity elements being ∧‎ and {∧‎} respectively (where ∧‎ is the empty string).
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