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Single Premise Post Canonical Forms Defined Over One-Letter Alphabets

Charles E. Hughes
The Journal of Symbolic Logic
Vol. 39, No. 3 (Sep., 1974), pp. 489-495
DOI: 10.2307/2272891
Stable URL: http://www.jstor.org/stable/2272891
Page Count: 7
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Single Premise Post Canonical Forms Defined Over One-Letter Alphabets
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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.

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