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On the convergence of query-bounded computations and logical closure properties of c.e. sets

Published online by Cambridge University Press:  12 March 2014

Timothy H. McNicholl
Timothy H. McNicholl*
Affiliation:
Department of Mathematics, University of Dallas, Irving, Texas 75062, USA, E-Mail: tmcnicho@acad.udallas.edu
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Abstract.

Call a set A n-correctable if every set Turing reducible to A via a Turing machine that on any input makes at most n queries is Turing reducible to A via a Turing machine that on any input makes at most n-queries and on any input halts no matter what answers are given to its queries. We show that if a c.e. set A is n-correctable for some n ≥ 2, then it is n-correctable for all n. We show that this is the optimal such result by constructing a c.e. set that is 1-correctable but not 2-correctable. The former result is obtained by examining the logical closure properties of c.e. sets that are 2-correctable.

Keywords

Bounded querieslogical closure propertiesadversaries
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 4 , December 2001 , pp. 1543 - 1560
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

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