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Single premise Post canonical forms defined over one-letter alphabets

Published online by Cambridge University Press:  12 March 2014

Charles E. Hughes
Charles E. Hughes*
Affiliation:
Pennsylvania State University, University Park, Pennsylvania 16802
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Abstract

In this paper we investigate some families of decision problems associated with a restricted class of Post canonical forms, specifically, those defined over one-letter alphabets whose productions have single premises and contain only one variable. For brevity sake, we call any such form an RPCF (Restricted Post Canonical Form). Constructive proofs are given which show, for any prescribed nonrecursive r.e. many-one degree of unsolvability D, the existence of an RPCF whose word problem is of degree D and an RPCF with axiom whose-decision problem is also of degree D. Finally, we show that both of these results are best possible in that they do not hold for one-one degrees.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 39 , Issue 3 , September 1974 , pp. 489 - 495
Copyright
Copyright © Association for Symbolic Logic 1974

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References

BIBLIOGRAPHY

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