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Monogenic normal systems are universal1

Published online by Cambridge University Press:  09 April 2009

Michael A. Arbib
Michael A. Arbib
Affiliation:
School of Mathematics, University of New South Wales and Department of Mathematics and Research Laboratory of Electronics, Massachusetts Institute of Technology.
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Abstract

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In 1943, Post conjectured that “monogenic normal systems are universal”, and in 1961 Minsky proved a stronger result “‘tag’ systems are universal” which implied the proof of Post's conjecture. The author had independently obtained a simple direct proof of Post's conjecture. The purpose of this note, then, is to present an exposition of Post's conjecture, and to show the full simplicity of its direct verification.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 3 , Issue 3 , August 1963 , pp. 301 - 306
Copyright
Copyright © Australian Mathematical Society 1963

References

[1]Davis, , Martin, , Computability and Unsolvability, McGraw-Hill, New York, 1958.Google Scholar
[2]Minsky, Marvin L., Recursive Unsolvability of the Problem of Tag, Annals of Math. 74, (1961), 437–455.CrossRefGoogle Scholar
[3]Post, Emil L., Formal Reductions of the General Combinatorial Decision Problem, Amer. J. Maths. 65 (1943), 197–215.CrossRefGoogle Scholar
[4]Turing, A. M., On Computable Numbers with an Application to the Entscheidungsproblem, Proc. London Math. Soc. (2) 42 (1936) 230–265; with a correction, Ibid. 43 (1936–7), 544–546.Google Scholar