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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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