GATE | GATE-CS-2014-(Set-3) | Question 46

Here, w^r is the reverse of the string w. Which of these languages are deterministic Context-free languages?

(A)

None of the languages

(B)

Only L1

(C)

Only L1 and L2

(D)

All the three languages

Answer: (C)

Explanation:

For L1 and L2 we can design Deterministic Pushdown automata, so both are DCFL. 
But for L3, it is not possible to design deterministic PDA, because DPDA cannot determine where \’w\’ ends exactly so it could start popping symbols (for w^r ) from the stack. 
Therefore, option (C) is Correct. 

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