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MoreCFL - Harvard CS 121 and CSCI E-207 Lecture 11: CFL...

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Harvard CS 121 and CSCI E-207 Lecture 11: CFL Closure Properties and Non-Context-Free Languages Harry Lewis October 8, 2009 Reading: Sipser, pp. 119-128.
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October 8, 2008 Closure Properties of CFLs Thm (last time): The CFLs are the languages accepted by PDAs Thm: The CFLs are closed under Union Concatenation Kleene * Intersection with a regular set 1
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October 8, 2008 The intersection of a CFL and a regular set is a CFL Pf sketch: Let L 1 be CF and L 2 be regular L 1 = L ( M 1 ) , M 1 a PDA L 2 = L ( M 2 ) , M 2 a DFA Q 1 = state set of M 1 Q 2 = state set of M 2 Construct a PDA with state set Q 1 × Q 2 which keeps track of computation of both M 1 and M 2 on input. 2
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October 8, 2008 Q: Why doesn’t this argument work if M 1 and M 2 are both PDAs? In fact, the intersection of two CFLs is not necessarily CF. And the complement of a CFL is not necessarily CF (PS4).
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MoreCFL - Harvard CS 121 and CSCI E-207 Lecture 11: CFL...

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