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The undecidability of the Turing machine immortality problem1

Published online by Cambridge University Press:  12 March 2014

Philip K. Hooper
Philip K. Hooper*
Affiliation:
Harvard University
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Extract

A Turing Machine (TM) is an abstract, synchronous, deterministic computer with a finite number of internal states. It operates on the set of infinite words, or tapes, over some finite alphabet, scanning exactly one symbol of the tape at a time. (Only a 2-symbol alphabet, consisting of “0” and “|”, will be considered here, and the scanned symbol of a tape will be distinguished by an underscore.) depending upon its internal state and the symbol under scan, it can perform one or more of the following operations: replace the scanned symbol with a new symbol, focus its attention on an adjacent square, and transfer control to a new state.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 2 , June 1966 , pp. 219 - 234
Copyright
Copyright © Association for Symbolic Logic 1966

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Footnotes

1

This paper was presented to the Division of Engineering and Applied Physics of Harvard University in partial fulfillment of the requirements for the Ph. D. degree in applied mathematics, and the work was supported, in part, by the Bell Telephone Laboratories, of Murray Hill. The author wishes to express his gratitude to Professor Hao Wang for inspiring and supervising this research.

References

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