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 there is 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:

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

Title alphabet
Canonical name Alphabet
Date of creation 2013-03-22 12:15:58
Last modified on 2013-03-22 12:15:58
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 7
Author mathcam (2727)
Entry type Definition
Classification msc 03C07
Synonym powers of an alphabet
Related topic KleeneStar
Related topic Substring
Related topic Language
Related topic HuffmanCoding
Related topic Word