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单词 Alphabet
释义

alphabet


An alphabet Σ is a nonempty finite setMathworldPlanetmath such that every string formed by elements of Σ can be decomposed uniquely into elements of Σ.

For example, {b,lo,g,bl,og}is not a valid alphabet because the string blog can be broken up in two ways: b lo g and bl og.{a,n¨a,d,a} is a valid alphabet, because thereis only one way to fully break up any given string formed from it.

If Σ is our alphabet and n+,we define the following as the powers of Σ:

  • Σ0=λ, where λ stands for the empty string.

  • Σn={xy|xΣ,yΣn-1} (xy is the juxtaposition of x and y)

So, Σn is the set of all strings formed from Σ of length n.

Titlealphabet
Canonical nameAlphabet
Date of creation2013-03-22 12:15:58
Last modified on2013-03-22 12:15:58
Ownermathcam (2727)
Last modified bymathcam (2727)
Numerical id7
Authormathcam (2727)
Entry typeDefinition
Classificationmsc 03C07
Synonympowers of an alphabet
Related topicKleeneStar
Related topicSubstring
Related topicLanguage
Related topicHuffmanCoding
Related topicWord
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更新时间:2025/5/4 17:25:46