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formal_language.md
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# Formal Language
The field of formal languages tries to [mathematically](math.md) and rigorously describe and examine anything that can be viewed as a language, which probably includes most structures we can think of, from human languages and computer languages to visual patterns and other highly abstract structures. Formal languages are at the root of theoretical [computer science](compsci.md) and are important e.g. for [computability](computability.md)/decidability, computational complexity, [security](security.md) and [compilers](compiler.md), but they also find use in linguistics and other fields of [science](science.md).
The field of formal languages tries to [mathematically](math.md) and rigorously examine and describe anything that can be viewed as a language, which probably includes most structures we can think of, from human languages and computer languages to visual patterns and other highly abstract structures. Formal languages are at the root of theoretical [computer science](compsci.md) and are important e.g. for [computability](computability.md)/decidability, computational complexity, [security](security.md) and [compilers](compiler.md), but they also find use in linguistics and other fields of [science](science.md).
A **formal language** is defined as a (potentially infinite) set of strings over some alphabet (which is finite). I.e. a language is a subset of E* where E is a finite alphabet (a set of *letters*). (* is a *Kleene Star* and signifies a set of all possible strings over E). The string belonging to a language may be referred to as a *word* or perhaps even *sentence*, but this word/sentence is actually a whole kind of *text* written in the language, if we think of it in terms of our natural languages.