Alphabet (computer science)

From Wikipedia, the free encyclopedia

In computer science, an alphabet is a finite set of characters or digits. The most common alphabet is {0,1}, the binary alphabet. A finite string is a finite sequence of characters from an alphabet; for instance a binary string is a string drawn from the alphabet {0,1}. An infinite sequence of characters may be constructed from elements of an alphabet as well.

Given an alphabet Σ, we write Σ * to denote the set of all finite strings over the alphabet Σ. Here, the * denotes the Kleene star operator. We write \Sigma^\infty (or occasionally, \Sigma^\N or Σω) to denote the set of all infinite sequences over the alphabet Σ.

For example, if we use the binary alphabet {0,1}, the strings {ε, 0, 1, 00, 01, 10, 11, 000, etc.) would all be in the Kleene closure of the alphabet (where ε represents the empty string)

Alphabets are important in the use of formal languages and automatons. Automatons such as Deterministic Finite Automatons (DFAs) require an alphabet in the formal definition. All states in a DFA must have a transition on every element in an alphabet.


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