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A simple solution of the uniform halting problem1

Published online by Cambridge University Press:  12 March 2014

Gabor T. Herman
Gabor T. Herman*
Affiliation:
IBM (UK) Education Centre, Greenford, Middlesex, England
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Extract

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]).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 4 , February 1970 , pp. 639 - 640
Copyright
Copyright © Association for Symbolic Logic 1970

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Footnotes

1

This paper has been presented to the Spring 1969 Meeting of the Association for Symbolic Logic, Cleveland, Ohio.

2

Present address: Department of Computer Science, State University of New York at Buffalo.

References

[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. 167–175.Google Scholar
[2] Hooper, P. K., The undecidability of the Turing machine immortality problem, this Journal , vol. 31 (1966), pp. 219–234.Google Scholar
[3] Minsky, M. L., Computation; finite and infinite machines, Prentice-Hall, Englewood Cliffs, N.J., 1967.Google Scholar