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

  • Timothy H. McNicholl (a1)

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.

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[1]Beigel, R., Gasarch, W., Kummer, M., Martin, G., McNicholl, T., and Stephan, F., On the query complexity of classes, Proceedings of the 21st international symposium, mathematical foundations of computer science, Lecture Notes in Computer Science, no. 1113, 1996, pp. 206217.
[2]Gasarch, W. and Martin, G., Bounded queries in recursion theory. Springer Verlag. New York. 1998.
[3]Soare, R. I., Recursively enumerable sets and degrees, 1st ed., Springer-Verlag, Berlin, Heidelberg, 1987.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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