Regular_Properties

Regular_Properties - P ro p e rtie s o f R e g ula rLa ng...

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Pro pe rtie s  o f  Re g ula r La ng ua g e s  
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1 L 2 L 2 1 L L C o nc a te nati o n: * 1 L S ta r: 2 1 L L Unio n: Are   re g ula r La ng uag e s Fo r re g ula r la ng uag e s         a nd        we  will pro ve  that: 1 L 2 1 L L C o m ple m e nt: Inte rs e c ti R L 1 Re ve rs a l:
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We  s a y:  Re g ular lang ua g e s  a re   closed under 2 1 L L C o nc ate na tio n: * 1 L S tar: 2 1 L L Unio n: 1 L 2 1 L L C o m ple m e nt: Inte rs e c tio n: R L 1 Re ve rs al:
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a b b a NFA Eq uivale nt  NFA λ a b b a A us e ful tra ns fo rm a tio n:  us e  o ne  a c c e pt s tate 2 ac c e pt s tate s 1 ac c e pt s ta te
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NFA Eq uivale nt NFA S ing le a c c e pting s tate λ In G e ne ra l
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NFA witho ut ac c e pting  s ta te Add an accepting state without transitions Extreme case
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1 L Regular language ( 29 1 1 L M L = 1 M Single accepting state NFA 2 M 2 L Single accepting state ( 29 2 2 L M L = Regular language NFA Take two languages
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} { 1 b a L n = a b 1 M { } ba L = 2 a b 2 M 0 n Example
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Union NFA for  1 M 2 M 2 1 L L λ
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  a b a b λ } { 1 b a L n = } { 2 ba L = } { } { 2 1 ba b a L L n = NFA for Example
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Concatenation NFA for  2 1 L L 1 M 2 M λ
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  NFA for a b a b } { 1 b a L n = } { 2 ba L = } { } }{ { 2 1 bba a ba b a L L n n = = λ Example
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Star Operation NFA for  * 1 L 1 M λ * 1 L 1 2 1 L w w w w w i k =
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NFA for * } { * 1 b a L n = a b } { 1 b a L n = λ Example
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This note was uploaded on 12/02/2011 for the course AR 107 taught by Professor Gracegraham during the Fall '11 term at Montgomery College.

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Regular_Properties - P ro p e rtie s o f R e g ula rLa ng...

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