Journal of Symbolic Logic

Inductive Inference and Unsolvability

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: 6 July 2007

http://projecteuclid.org/euclid.jsl/1183743737

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