Which of the following is not decidable?

1997

Which of the following is not decidable?

  1. A.

    Given a Turing machine M, a string s and an integer k, M accepts s within k steps

  2. B.

    Equivalence of two given Turing machines

  3. C.

    Language accepted by a given finite state machine is not empty

  4. D.

    Languages generated by a context free grammar is non empty

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Correct answer: B

To determine decidability, we analyze each problem. Simulating a Turing machine for fixed steps always halts, making it decidable. Checking emptiness for Finite State Machines and Context-Free Grammars is also algorithmically solvable. However, determining if two Turing machines accept the same language is undecidable, as it can be reduced from the Halting Problem.

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