Richard Beigel

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Prior results show that most bounded query hierarchies cannot

contain finite gaps. For example, it is known that

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P<sub>(<i>m</i>+1)-tt</sub><sup>SAT</sup> = P<sub><i>m</i>-tt</sub><sup>SAT</sup> implies P<sub>btt</sub><sup>SAT</sup> = P<sub><i>m</i>-tt</sub><sup>SAT</sup>

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and for all sets <i>A</i>

<ul>

<li> FP<sub>(<i>m</i>+1)-tt</sub><sup><i>A</i></sup> = FP<sub><i>m</i>-tt</sub><sup><i>A</i></sup> implies FP<sub>btt</sub><sup><i>A</i></sup> = FP<sub><i>m</i>-tt</sub><sup><i>A</i></sup>

</li>

<li> P<sub>(<i>m</i>+1)-T</sub><sup><i>A</i></sup> = P<sub><i>m</i>-T</sub><sup><i>A</i></sup> implies P<sub>bT</sub><sup><i>A</i></sup> = ...
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Denis Xavier Charles

We show that there are infinitely many primes $p$, such

that the subgroup membership problem for PSL(2,p) belongs

to $\NP \cap \coNP$.

Parikshit Gopalan, Venkatesan Guruswami

We study the average-case hardness of the class NP against

deterministic polynomial time algorithms. We prove that there exists

some constant $\mu > 0$ such that if there is some language in NP

for which no deterministic polynomial time algorithm can decide L

correctly on a $1- (log n)^{-\mu}$ fraction ...
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Christian Glaßer, Maximilian Witek

We study the autoreducibility and mitoticity of complete sets for NP and other complexity classes, where the main focus is on logspace reducibilities. In particular, we obtain:

- For NP and all other classes of the PH: each logspace many-one-complete set is logspace Turing-autoreducible.

- For P, the delta-levels of ...
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Stephen Cook, Bruce Kapron

This paper is a transcription of mimeographed course notes titled ``A Survey of Classes of Primitive Recursive Functions", by S.A. Cook, for the University of California Berkeley course Math 290, Sect. 14, January 1967. The notes present a survey of subrecursive function

classes (and classes of relations based on these ...
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