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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:
 Strings produced by some formal grammar (see Chomsky hierarchy);
 Strings described or matched by a regular expression;
 Strings accepted by some automaton, such as a Turing machine or finite state automaton;
 Strings indicated by a decision procedure (a set of related YES/NO questions) where the answer is YES.
Related pages
 Language for languages in general
 Syntax for the form of a language in general
 Semantics for the meanings in a language
 Natural language for languages that are not formal
 Computer language for application of formal languages in computing
 Programming language for the application of formal languages to program computers
Further reading
 Hopcroft, J. & Ullman, J. (1979). Introduction to Automata Theory, Languages, and Computation. AddisonWesley.
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 Helena Rasiowa and Roman Sikorski (1970). The Mathematics of Metamathematics (3^{rd} ed. ed.). PWN., chapter 6 Algebra of formalized languages.
 Rozemberg, G. & Salomaa, A. (eds.) (1979). Introduction to Automata Theory, Languages, and Computation. AddisonWesley.
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Other websites
 http://icalp06.dsi.unive.it/ ICALP 2006 33rd International Colloquium on Automata, Languages and Programming.
 http://www.cs.auckland.ac.nz/CDMTCS/conferences/dlt/DLTConfSeries.html International Conferences on Developments in Language Theory
