Monogenic Post Normal Systems of Arbitrary Degree

  • Authors:

  • Philip K. Hooper

  • Affiliations:

  • Computation Laboratory, Harvard University, Cambridge, Massachusetts

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1966

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Abstract

From an arbitrary Turing machine, Z, a monogenic Post normal system, v(Z), is constructed. It is then shown not only that the halting problem for Z is reducible to that of v(Z) but also that the halting problem for v(Z) is reducible to that of Z. Since these two halting problems are of the same degree, the halting problem for the normal system can have an arbitrary (recursively enumerable) degree of undecidability.