Richard Beigel, William Gasarch, Efim Kinber

For a set A and a number n let F_n^A(x_1,...,x_n) =

A(x_1)\cdots A(x_n). We study how hard it is to approximate this

function in terms of the number of queries required. For a general

set A we have exact bounds that depend on functions from coding

theory. These are applied ...
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Manindra Agrawal, Richard Beigel, Thomas Thierauf

The classes of languages accepted by nondeterministic polynomial-time

Turing machines (NP machines, in short) that have restricted access to

an NP oracle --- the machines can ask k queries to the NP oracle and

the answer they receive is the number of queries ...
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Richard Beigel

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Prior results show that most bounded query hierarchies cannot

contain finite gaps. For example, it is known that

<center>

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>

</center>

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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Amihood Amir, Richard Beigel, William Gasarch

Let A(x) be the characteristic function of A. Consider the function

F_k^A(x_1,...,x_k) = A(x_1)...A(x_k). We show that if F_k^A can be

computed with fewer than k queries to some set X, then A can be

computed by polynomial size circuits. A generalization of this result

has applications to bounded query ...
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Richard Beigel, Harry Buhrman, Peter Fejer, Lance Fortnow, Piotr Grabowski, Luc Longpré, Andrej Muchnik, Frank Stephan, Leen Torenvliet

A recursive enumerator for a function $h$ is an algorithm $f$ which

enumerates for an input $x$ finitely many elements including $h(x)$.

$f$ is an $k(n)$-enumerator if for every input $x$ of length $n$, $h(x)$

is among the first $k(n)$ elements enumerated by $f$.

If there is a $k(n)$-enumerator for ...
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