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Regular language
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== Formal definition == The collection of regular languages over an [[Alphabet (formal languages)|alphabet]] Ξ£ is defined recursively as follows: * The empty language β is a regular language. * For each ''a'' β Ξ£ (''a'' belongs to Ξ£), the [[Singleton (mathematics)|singleton]] language {{mset|''a''}} is a regular language. * If ''A'' is a regular language, ''A''* ([[Kleene star]]) is a regular language. Due to this, the empty string language {{mset|Ξ΅}} is also regular. * If ''A'' and ''B'' are regular languages, then {{nowrap|''A'' βͺ ''B''}} (union) and {{nowrap|''A'' β’ ''B''}} (concatenation) are regular languages. * No other languages over Ξ£ are regular. See ''{{slink|Regular expression#Formal language theory}}'' for syntax and semantics of regular expressions.
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