GATE | GATE MOCK 2017 | Question 54

Suppose M1 and M2 are two TM’s such that L(M1) = L(M2). Then

(A) On every input on which M1 doesn’t halt, M2 doesn’t halt too.

(B) On every i/p on which M1 halts, M2 halts too.

(C) On every i/p which M1 accepts, M2 halts.

(D) None of above.

Answer: (C)


M2 accepts strings in L(M1) so definitely it will halt. Other 2 are not guaranteed as Turing machine M does not accept w if it either rejects w by halting to a reject state or loops infinitely on w.

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