Abstract
In this chapter we examine sets A such that (∃n ≥ l)[Q(n, A) = QC(n,A)]. Of course, for every set A we have that (∀n ≥ l)[QC(n, A) Q(n,A)]. Thus here we are studying sets A such that (∃n ≥ l )[Q(n, A) QC(n, A)]. This condition holds of a set A iff there is some n ≥ 1 with the property that, for every set B ∈ Q(n, A): there is an oracle Turing machine M() for deciding B with n queries to A such that, for all x,X, the Mx(x) computation converges after making at most n queries to X. This is equivalent to saying that MA decides B with n queries to A and, for every x and every string σ ∈ {0,1}n, the Mσ(x) computation converges (see Notation 1.2.19)
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© 1999 Springer Science+Business Media New York
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Gasarch, W.I., Martin, G.A. (1999). Q Versus QC. In: Bounded Queries in Recursion Theory. Progress in Computer Science and Applied Logic, vol 16. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0635-4_7
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DOI: https://doi.org/10.1007/978-1-4612-0635-4_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6848-2
Online ISBN: 978-1-4612-0635-4
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