Journal of Symbolic Logic

Inductive Inference and Unsolvability

Leonard M. Adleman and M. Blum

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Abstract

It is shown that many different problems have the same degree of unsolvability. Among these problems are: THE INDUCTIVE INFERENCE PROBLEM. Infer in the limit an index for a recursive function $f$ presented as $f(0), f(1), f(2),\ldots$. THE RECURSIVE INDEX PROBLEM. Decide in the limit if $i$ is the index of a total recursive function. THE ZERO NONVARIANT PROBLEM. Decide in the limit if a recursive function $f$ presented as $f(0), f(1), f(2),\ldots$ has value unequal to zero for infinitely many arguments. Finally, it is shown that these unsolvable problems are strictly easier than the halting problem.

Article information

Source
J. Symbolic Logic Volume 56, Issue 3 (1991), 891-900.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1183743737

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.2178/jsl/1183743737

Mathematical Reviews number (MathSciNet)
MR1129153

Zentralblatt MATH identifier
0751.03018

Citation

Adleman, Leonard M.; Blum, M. Inductive Inference and Unsolvability. J. Symbolic Logic 56 (1991), no. 3, 891--900. doi:10.2178/jsl/1183743737. http://projecteuclid.org/euclid.jsl/1183743737.


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