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A simple solution of the uniform halting problem1

  • Gabor T. Herman (a1)

The uniform halting problem (UH) can be stated as follows.

Give a decision procedure which for any given Turing machine (TM) will decide whether or not it has an immortal instantaneous description (ID).

An ID is called immortal if it has no terminal successor. As it is generally the case in the literature (see e.g. Minsky [3, p. 118]) we assume that in an ID the tape must be blank except for some finite numbers of squares. If we remove this restriction the UH becomes the immortality problem (IP). The UH should not be confused with the initialised uniform halting problem (whether or not a TM has an immortal ID when started in a specified state) which can easily be shown to be undecidable (see e.g. Minsky [3, p. 151]).

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[1]Davis, M. D., A note on universal Turing machines. Automata studies, Annals of Mathematical Studies, no. 34, Princeton Univ. Press, Princeton, N.J., 1956, pp. 167175.
[2]Hooper, P. K., The undecidability of the Turing machine immortality problem, this Journal, vol. 31 (1966), pp. 219234.
[3]Minsky, M. L., Computation; finite and infinite machines, Prentice-Hall, Englewood Cliffs, N.J., 1967.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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