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# Formal language

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A formal language is a set of words over some finite alphabet, like `ababba` over the alphabet {`a`,`b`}. The empty word is usually denoted by e or epsilon.

Typical examples of formal languages would be the set of all words over {`a`,`b`}, the set {`a`n|n is prime}, the set of syntactically correct programs in some programming language, or the set of inputs upon which a certain Turing machine halts.

Formal languages can be defined in a great variety of ways, such as being produced by some formal grammar, being accepted by some Turing machine or some sort of automaton, or being some suitable encoding of a combinatiorial problem.

A typical questions asked about a formal language is how difficult it is to decide whether a given word belongs to the language. This is the domain of [computability theory]? and [complexity theory]?.

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Last edited August 2, 2001 7:25 am (diff)
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