is the halting problem semi decidable


Theorem: the non-acceptance problem NAP and the non-halting problem NHP are not semi-decidable. Proof: if both a problem and its complement were semi-decidable,  Questions d'autres utilisateurs
  • Is the halting problem semi-decidable?

    The halting problem and the acceptance problem are “equivalent”. Theorem: the halting problem HP is semi-decidable. Proof: we construct Turing machine M which takes (?M?,w) and simulates the execution of M on input w. If (the simulation of) M halts, M accepts its input.
  • Is semi-decidable decidable?

    Every decidable theory or logical system is semidecidable, but in general the converse is not true; a theory is decidable if and only if both it and its complement are semi-decidable. For example, the set of logical validities V of first-order logic is semi-decidable, but not decidable.
  • What is a semi-decidable problem?

    Definition. A problem (D,Q) is semi-decidable if there is a TM/RM that returns “yes” for any d ? Q, but may return “no” or loop forever when d /? Q. Semi-decidable problems are sometimes called recognisable.
  • The halting problem is partially computable
    (p, x) ? HALT.
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