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- Amihood Amir, Richard Beigel, William I. Gasarch
- Structure in Complexity Theory Conference
- 1990

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)

- William Gasarch
- 2004

e will onsider lter formultion y ghor et lF PQF e model dtse s @IA n nE it string x = x 1 x 2 · · · x n D together with @PA omputtionl gent tht n do omputtions sed on oth x nd queries mde to itF elie wnts to otin x i suh tht the dtse does not lern iF etully elie wnts more thn tht! she wnts the dtse… (More)

- William I. Gasarch, Evan Golub, Aravind Srinivasan
- Theor. Comput. Sci.
- 2003

- Richard Beigel, William I. Gasarch, John Gill, James C. Owings
- Inf. Comput.
- 1993

- William I. Gasarch
- Structure in Complexity Theory Conference
- 1991

- Richard Chang, William I. Gasarch, Carsten Lund
- SIAM J. Comput.
- 1993

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)

A two-dimensional grid is a set G n,m = [n] × [m]. A grid G n,m is c-colorable if there is a function χ n,m : G n,m → [c] such that there are no rectangles with all four corners the same color. We address the following question: for which values of n and m is G n,m c-colorable? This problem can be viewed as a bipartite Ramsey problem and is related to the… (More)

- Richard Beigel, William I. Gasarch
- Ann. Pure Appl. Logic
- 1989

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)

- William I. Gasarch, Mark W. Krentel, Kevin J. Rappoport
- Mathematical Systems Theory
- 1995

- Richard Beigel, William I. Gasarch
- Discrete Applied Mathematics
- 1991

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)