Mathematische Annalen

, Volume 152, Issue 1, pp 65–74 | Cite as

Tag systems and lag systems

  • Hao Wang


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  1. [1]
    Minsky, M. L.: Recursive unsolvability of Post's problem of Tag. Ann. Math.74, 437–455 (1961).Google Scholar
  2. [2]
    --Universality of (p=2) Tag systems. A. I. Memo No. 33, Cambridge, Mass. (1962). A modified version of this (Memo No. 52, April 1963) has been prepared byCocke andMinsky for publication. This new proof is such that a simple modification would yield Theorem 5 above.Google Scholar
  3. [3]
    Post, E. L.: Formal reduction of the general combinatorial decision problem. Am. J. Math.65, 197–215 (1943).Google Scholar
  4. [4]
    Shepherdson, J. C., andH. E. Sturgis: The computability of partial recursive functions by forms of turing machines. Abstracts, International Congress for Logic, Methodology and Philosophy of Science, Stanford, California (1960), p. 17. The full paper has just appeared as “Computability of recursive functions”, Journal of Association for Computing Machinery10, 217–255 (1963).Google Scholar
  5. [5]
    Wang, Hao: A variant to Turing's theory of computing machines. Journal of Association for Computing Machinery4, 63–92 (1957).Google Scholar
  6. [6]
    --Tag systems and lag systems. (Abstract) Notices of the Am. Math. Soc.9, 407 (1962).Alan Tritter has recently made use of results in [2] and [6] to obtain a universal Turing machine with 4 symbols and 6 states, the smallest at present.Google Scholar

Copyright information

© Springer-Verlag 1963

Authors and Affiliations

  • Hao Wang
    • 1
  1. 1.Cambridge

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