Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 56, Issue 3 (1991), 891-900.
Inductive Inference and Unsolvability
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.
J. Symbolic Logic Volume 56, Issue 3 (1991), 891-900.
First available in Project Euclid: 6 July 2007
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Adleman, Leonard M.; Blum, M. Inductive Inference and Unsolvability. J. Symbolic Logic 56 (1991), no. 3, 891--900. doi:10.2178/jsl/1183743737. https://projecteuclid.org/euclid.jsl/1183743737.