Skip to content
Related Articles

Related Articles

Improve Article
GATE | GATE-CS-2007 | Question 30
  • Last Updated : 24 Feb, 2014

The language L= {0i21i | i≥0 } over the alphabet {0,1, 2} is:
(A) not recursive
(B) is recursive and is a deterministic CFL.
(C) is a regular language.
(D) is not a deterministic CFL but a CFL.


Answer: (B)

Explanation: Let us first design a deterministic pushdown automata for the given language.

  • For each occurrence of ‘0’ , we PUSH X in the stack.
  • When ‘2’ appears, no stack operation is performed. But, state of the automata is changed.
  • For each occurrence of ‘1’ , we POP X from the stack.
  • If at the end Z0 is on the stack top then input string is accepted

We also design a Turing machine for the given language.

  • When ‘0’ appears in the input string , we replace it with X .Then, traverse to the rightmost corner and replace ‘1’ with Y.
  • We go back to the leftmost ‘0’ and repeat the above process.
  • While traversing rightwards from the beginning of the input string, if after X, ‘2’ appears and after ‘2’, Y appears then we reach the HALT state.

    Thus, the given language is recursive. Every recursive language is a CFL.
    Thus, option (B) is the answer.

    Please comment below if you find anything wrong in the above post.


Quiz of this Question

Attention reader! Don’t stop learning now. Learn all GATE CS concepts with Free Live Classes on our youtube channel.

My Personal Notes arrow_drop_up
Recommended Articles
Page :