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Regular_Expressions

# Regular_Expressions - R e g ula rExp re s s io ns...

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Re g ula r Expre s s io ns

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Regular Expressions Regular expressions  describe regular languages   Example:                  describes the language * ) ( c b a + { } { } ,... , , , , , * , bca abc aa bc a bc a λ =
Recursive Definition α λ , , ( 29 1 1 2 1 2 1 * r r r r r r + Are regular expressions Primitive regular expressions: 2 r 1 r Given regular expressions       and

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Examples ( 29 ) ( * + + c c b a A regular expression: ( 29 + + b a Not a regular expression:
Languages of Regular Expressions                   :   language of regular expression Example   ( 29 r L r ( 29 { } ,... , , , , , * ) ( bca abc aa bc a c b a L λ = +

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Definition For primitive regular expressions: ( 29 ( 29 { } ( 29 { } a a L L L = = = λ
Definition (continued) For regular expressions       and    1 r 2 r ( 29 ( 29 ( 29 2 1 2 1 r L r L r r L = + ( 29 ( 29 ( 29 2 1 2 1 r L r L r r L = ( 29 ( 29 ( 29 * * 1 1 r L r L = ( 29 ( 29 ( 29 1 1 r L r L =

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Example Regular expression:   ( 29 * a b a + ( 29 ( 29 * a b a L + ( 29 ( 29 ( 29 * a L b a L + = ( 29 ( 29 * a L b a L + = ( 29 ( 29 ( 29 ( 29 ( 29 * a L b L a L = { } { } ( 29 { } ( 29 * a b a = { } { } ,... , , , , aaa aa a b a λ = { } ,... , , ,..., , , baa ba b aaa aa a =
Example Regular expression  ( 29 ( 29 bb a b a r + + = * ( 29 { } ,... , , , , , bbb ba abb aa bb a r L =

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Example Regular expression ( 29 ( 29 b bb aa r * * = ( 29 } 0 , : { 2 2 = m n b b a r L m n
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Regular_Expressions - R e g ula rExp re s s io ns...

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