lecture 38
Post on 31-Dec-2015
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1
Lecture 38
• Showing CFL’s not closed under set intersection and set complement
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Nonclosure Properties for CFL’s
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CFL’s not closed under set intersection
• How do we prove that CFL’s are not closed under set intersection?– State closure property as IF-THEN statement
• If L1 and L2 are CFL’s, then L1 intersect L2 is a CFL
– Proof is by counterexample• Find 2 CFL’s L1 and L2 such that L1 intersect L2 is
NOT a CFL
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Counterexample
• What is a possible L1 intersect L2?
– What non-CFL languages do we know?
• What could L1 and L2 be?
– L1 =
– L2 =
– How can we prove that L1 and L2 are context-free?
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CFL’s not closed under complement
• How can we prove that CFL’s are not closed under complement?– We could do the same thing, find a
counterexample– Another way
• Use fact that any language class which is closed under union and complement must also be closed under intersection
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Language class hierarchy
All languages over alphabet
RE
REG
HH
EqualCFLREC
Equal-3
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