Journal of Symbolic Logic

Inductive Inference and Unsolvability

Leonard M. Adleman and M. Blum

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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.

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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.

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