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.
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