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Which of the following is decidable ?

  • A.HALTING PROBLEM of TM
  • B.EMPTINESS PROBLEM of TM
  • C.EQUIVALENCE OF DFA
  • D.EQUIVALENCE OF TM

Answer: C

The decidable problem is EQUIVALENCE OF DFA.

Whether two DFAs accept the same language can be decided: minimise both and compare them, or build a DFA for the symmetric difference of their languages and test it for emptiness, which is a simple reachability check.

The halting problem for Turing machines is the classic undecidable problem. Emptiness and equivalence of Turing machines are undecidable as well, by Rice's theorem, since each asks a non-trivial question about the language a TM accepts.

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