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. Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... In computer programming and formal language theory, (and other branches of mathematics), a string is an ordered sequence of symbols. ... This is a page about mathematics. ...

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 (or occasionally, or Σ^ω) to denote the set of all infinite sequences over the alphabet Σ. In mathematical logic and computer science, the Kleene star (or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters. ...

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) In various branches of mathematics and computer science, strings are sequences of various simple objects (symbols, tokens, characters, etc. ...

Alphabets are important in the use of formal languages, automatons and semiautomatons. Automatons, such as deterministic finite automatons (DFAs), require an alphabet in the formal definition. In mathematics, logic and computer science, a formal language is a set of finite-length words (i. ... In theoretical computer science, automata theory is the study of abstract machines and problems they are able to solve. ... It has been suggested that state transition system be merged into this article or section. ... In the theory of computation, a deterministic finite state machine or deterministic finite automaton (DFA) is a finite state machine where for each pair of state and input symbol there is a deterministic next state. ...

See also

• Formal language
• Syntax
• Semantics