Module 37

1
Module 37

• Showing CFLs not closed under set intersection
  and set complement

2
Nonclosure Properties for CFLs
3
CFLs not closed under set intersection

• How can we prove that CFLs are not closed under
  set intersection?

4
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?

5
CFLs not closed under complement

• How can we prove that CFLs are not closed under
  complement?
• Another way
• Use fact that any language class which is closed
  under union and complement must also be closed
  under intersection

6
Language class hierarchy
REG