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Formal language




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In mathematics, a formal language is one that has a particular set of symbols that are made according to a particular kind of rule.

Examples

Some examples of formal languages:

  • the set of all words over [math]{a, b}\,[/math]
  • the set [math]\left \{ a^{n}\right\}[/math], where [math]n\,[/math] is a natural number and [math]a^n\,[/math] means [math]a\,[/math] repeated [math]n\,[/math] times
  • finite languages, such as [math]\{\{a,b\},\{a, aa, bba\}\}\,[/math]
  • the set of syntactically correct programs in a given programming language; or
  • the set of inputs upon which a certain Turing machine halts.

Specification

A formal language can be specified in a great variety of ways, such as:

Related pages

Further reading

  • Hopcroft, J. & Ullman, J. (1979). Introduction to Automata Theory, Languages, and Computation. Addison-Wesley. ISBN 0-201-02988-X
      . 
  • Helena Rasiowa and Roman Sikorski (1970). The Mathematics of Metamathematics (3rd ed. ed.). PWN. , chapter 6 Algebra of formalized languages.
  • Rozemberg, G. & Salomaa, A. (eds.) (1979). Introduction to Automata Theory, Languages, and Computation. Addison-Wesley. ISBN 978-3-540-61486-9
      . 

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