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Inductive inference and unsolvability

Published online by Cambridge University Press:  12 March 2014

Leonard M. Adleman and
M. Blum
Leonard M. Adleman
Affiliation:
Department of Computer Science, University of Southern California, Los Angeles, California 90089-0782
M. Blum
Affiliation:
Department of Electrical Engineering and Computer Sciences, and the Electronics Research Laboratory, University of California, Berekeley, California 94720
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Abtract

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),….

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),… has value unequal to zero for infinitely many arguments.

Finally, it is shown that these unsolvable problems are strictly easier than the halting problem.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 56 , Issue 3 , September 1991, pp. 891 - 900
Copyright
Copyright © Association for Symbolic Logic 1991

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References

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