GATE2001-1.5

Question

Which of the following statements is true?

• A. If a language is context free it can always be accepted by a deterministic push-down automaton
• B. The union of two context free languages is context free
• C. The intersection of two contest free languages is a context free
• D. The complement of a context free language is a context free

Answer 1

Answer is (B).

(A) is wrong as a language can be context free even if it is being accepted by non-deterministic PDA for ex- $\{ ww^r: w \in \Sigma^*$ and $w^r$  is reverse of $w\}$

(C) and (D) not always true as Context free languages are not closed under Complement or Intersection.

Comments

I think example of A is wrong ... it will be { WW^r  :  W ∈(a,b)⁺ and W^r  is reverse} ... correct me if i am wrong ...

Edit : { WW^r  :  W ∈(a,b)^* and W^r  is reverse}  ... both r npda .... My mistake ...

Answer 2

Ans: B not closed under intersection and complement