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‡e will ™onsider — l—ter formul—tion ˜y ghor et —lF ‘PQ“F ‡e model — d—t—˜—se —s @IA —n nE ˜it string x = x 1 x 2 · · · x n D together with @PA — ™omput—tion—l —gent th—t ™—n do ™omput—tions ˜—sed on ˜oth x —nd queries m—de to itF eli™e w—nts to o˜t—in x i su™h th—t the d—t—˜—se does not le—rn iF e™tu—lly eli™e w—nts more th—n th—t! she w—nts the d—t—˜—se(More)
Consider the function F A k (x 1 ; : : :; x k) = A(x 1) A(x k). We show that if F A k can be computed with less than k queries to some set X then A 2 P=poly. A generalization of this result has applications to bounded query classes, circuits, and enumerability. In particular we obtain the following. (1) Assuming p 3 6 = p 3 the hierarchy of functions(More)
This paper investigates the computational complexity of approximating several NP-optimization problems using the number of queries to an NP oracle as a complexity measure. The results show a trade-off between the closeness of the approximation and the number of queries required. For an approximation factor k(n), log log k(n) n queries to an NP oracle can be(More)
We classify functions in recursive graph theory in terms of how many queries to K (or ∅ ′′ or ∅ ′′′) are required to compute them. We show that (1) binary search is optimal (in terms of the number of queries to K) for finding the chromatic number of a recursive graph and that no set of Turing degree less than 0 ′ will suffice, (2) determining if a recursive(More)
Let x 1 ,. .. , x k be n-bit numbers and T ∈ N. Assume that P 1 ,. .. , P k are players such that P i knows all of the numbers except x i. The players want to determine if k j=1 x j = T by broadcasting as few bits as possible. Chandra, Furst, and Lipton obtained an upper bound of O(√ n) bits for the k = 3 case, and a lower bound of ω(1) for k ≥ 3 when T =(More)
1) Introduction We examine the problem of coloring part of a k-colorable graph, while not knowing the rest of it. To illustrate some of our concepts, we describe a somewhat whimsical scenario, which we call the Mapmaker's Dilemma. Picture a 12th-century mapmaker who is given a map of Europe and the countries adjacent to Europe, and is told to 4-color the(More)
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract. Suppose that a and d are positive integers with a ≥ 2. Let h a,d(More)