14_Context_Free_Properties.pdf - Properties of Context-Free languages Union Context-free languages are closed under Union L1 is context free L1 L2 L2 is

14_Context_Free_Properties.pdf - Properties of Context-Free...

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Properties of Context-Free languages
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Context-free languages are closed under: Union 1 L is context free 2 L is context free 2 1 L L is context-free Union
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Example | 1 1 b aS S | | 2 2 2 b bS a aS S Union } { 1 n n b a L } { 2 R ww L 2 1 | S S S } { } { R n n ww b a L Language Grammar
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In general: The grammar of the union has new start variable and additional production 2 1 | S S S For context-free languages with context-free grammars and start variables 2 1 , L L 2 1 , G G 2 1 , S S 2 1 L L S
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Context-free languages are closed under: Concatenation 1 L is context free 2 L is context free 2 1 L L is context-free Concatenation
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Example | 1 1 b aS S | | 2 2 2 b bS a aS S Concatenation } { 1 n n b a L } { 2 R ww L 2 1 S S S } }{ { R n n ww b a L Language Grammar
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In general: The grammar of the concatenation has new start variable and additional production 2 1 S S S For context-free languages with context-free grammars and start variables 2 1 , L L 2 1 , G G 2 1 , S S 2 1 L L S
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Context-free languages are closed under: Star-operation L is context free * L is context-free Star Operation
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  • Fall '19
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