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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

Alice wants to query a database but she does not want the database to learn what she is querying. She can ask for the entire database. Can she get her query answered with less communication? One model of this problem is Private Information Retrieval , henceforth PIR. We survey results obtained about the PIR model including partial answers to the following… (More)

- Amihood Amir, William I. Gasarch
- Inf. Comput.
- 1987

- William I. Gasarch, Carl H. Smith
- J. ACM
- 1988

Traditional work in inductive inference has been to model a learner receiving data about a function <italic>f</italic> and trying to learn the function. The data is usually just the values <italic>f</italic>(0), <italic>f</italic>(1),…. The scenario is modeled so that the learner is also allowed to ask questions about the data (e.g.,… (More)

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

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

- William I. Gasarch, Mark G. Pleszkoch
- COLT
- 1989

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

This paper investigates the computational complexity of approximating several NPoptimization 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 logk(n) n queries to an NP oracle can be… (More)

- Richard Beigel, William I. Gasarch, Louise Hay
- Arch. Math. Log.
- 1989

Let A be any nonrecursive set. We deene a hierarchy of sets (and a corresponding hierarchy of degrees) that are reducible to A based on bounding the number of queries to A that an oracle machine can make. When A is the halting problem K our hierarchy of sets interleaves with the diierence hierarchy 1 on the r.e. sets in a logarithmic way; this follows from… (More)

- Dana Angluin, William I. Gasarch, Carl H. Smith
- Theor. Comput. Sci.
- 1989