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Unformatted text preview: 1 Module 31 Closure Properties for CFLs Kleene Closure Union Concatenation CFLs versus regular languages regular languages subset of CFL 2 Closure Properties for CFLs Kleene Closure 3 CFL closed under Kleene Closure Let L be an arbitrary CFL Let G 1 be a CFG s.t. L(G 1 ) = L G 1 exists by definition of L 1 in CFL Construct CFG G 2 from CFG G 1 Argue L(G 2 ) = L * There exists CFG G 2 s.t. L(G 2 ) = L * L * is a CFL 4 Visualization L * L CFL CFGs Let L be an arbitrary CFL Let G 1 be a CFG s.t. L(G 1 ) = L G 1 exists by definition of L 1 in CFL Construct CFG G 2 from CFG G 1 Argue L(G 2 ) = L * There exists CFG G 2 s.t. L(G 2 ) = L * L * is a CFL G 1 G 2 5 Algorithm Specification Input CFG G 1 Output CFG G 2 such that L(G 2 ) = CFG G 1 CFG G 2 A 6 Construction Input CFG G 1 = (V 1 , , S 1 , P 1 ) Output CFG G 2 = (V 2 , , S 2 , P 2 ) V 2 = V 1 union {T} T is a new symbol not in V 1 or S 2 = T P 2 = P 1 union ?? 7 Closure Properties for CFLs Kleene Closure Examples 8...
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 Fall '07
 TORNG

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