1 Module 37 Showing CFL’s not closed under set intersection and set complement

2 Nonclosure Properties for CFL’s

3 CFL’s not closed under set intersection * How can we prove that CFL’s are not closed under set intersection?

4 Counterexample * What is a possible L 1 intersect L 2 ? –What non-CFL languages do we know? What could L 1 and L 2 be? –L 1 = –L 2 = –How can we prove that L 1 and L 2 are context- free?

5 CFL’s not closed under complement * How can we prove that CFL’s 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 All languages over alphabet  RE REG H H Equal CFL REC Equal-3