skip to main content
research-article
Open Access

X-machines and the halting problem: Building a super-turing machine

Published:01 March 1990Publication History
Skip Abstract Section

Abstract

Abstract

We describe a novel machine model of computation, and prove that this model is capable of performing calculations beyond the capability of the standard Turing machine model. In particular, we demonstrate the ability of our model to solve the Halting problem for Turing machines. We discuss the issues involved in implementing the model as a physical device, and offer some tentative suggestions.

References

  1. [Cou54] Coulson, C. A.:Electricity. Oliver and Boyd, 1954.Google ScholarGoogle Scholar
  2. [Cro76] Cross, R. C.:Electricity and Magnetism. Longman, 1976.Google ScholarGoogle Scholar
  3. [Cut80] Cutland, N. J.:Computability. Cambridge University Press, 1980.Google ScholarGoogle Scholar
  4. [Deu85] Deutsch D.Quantum Theory, the Church-Turing Principle and the Universal Quantum ComputerProc. Royal Soc.1985A40087117Google ScholarGoogle Scholar
  5. [Deu89] Deutsch, D.: Quantum Communication Thwarts Eavesdroppers.New Scientist, 9 December (1989).Google ScholarGoogle Scholar
  6. [Ei174] Eilenberg, S.:Automata, Languages, and Machines, vol. A. Academic Press, 1974.Google ScholarGoogle Scholar
  7. [Ho187] Holcombe W. M. L.Formal Methods in the Specification of the Human-Computer InterfaceInt. CIS J.1987122436Google ScholarGoogle Scholar
  8. [Ho188] Holcombe W. M. L.X-machines as a Basis for System SpecificationSoft. Eng. J.1988326976Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. [Pen89] Penrose, R.:The Emperor's New Mind. Oxford University Press, 1989.Google ScholarGoogle Scholar
  10. [RoB81] Roberts, A. and Bush, B. (eds):Neurones without Impulses. Cambridge University Press, 1981.Google ScholarGoogle Scholar
  11. [Wei73] Weir, A. J.:Lebesgue Integration and Measure. Cambridge University Press, 1973.Google ScholarGoogle Scholar
  12. [Wi170] Willard, S.:General Topology. Addison-Wesley, 1970.Google ScholarGoogle Scholar

Index Terms

  1. X-machines and the halting problem: Building a super-turing machine
            Index terms have been assigned to the content through auto-classification.

            Recommendations

            Comments

            Login options

            Check if you have access through your login credentials or your institution to get full access on this article.

            Sign in

            Full Access

            • Article Metrics

              • Downloads (Last 12 months)39
              • Downloads (Last 6 weeks)6

              Other Metrics

            PDF Format

            View or Download as a PDF file.

            PDF

            eReader

            View online with eReader.

            eReader