GATE | GATE CS 1996 | Question 9

Which of the following statements is false?

(A) The Halting Problem of Turing machines is undecidable
(B) Determining whether a context-free grammar is ambiguous is undecidable
(C) Given two arbitrary context-free grammars G1 and G2 it is undecidable whether L(G1)=L(G2)
(D) Given two regular grammars G1 and G2 it is undecidable whether L(G1)=L(G2)


Answer: (D)

Explanation: Halting problem of Turing Machine is undecidable because there is no algorithm exists for it.

Determining a context free language is ambiguous is undecidable because no algorithm exists to decide CFG is ambiguous.
Equivalence problem of CFG is undecidable.
Everything about regular language is decidable.

Option (D) is correct.

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