William I. Gasarch

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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)
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)
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),&#8230;. The scenario is modeled so that the learner is also allowed to ask questions about the data (e.g.,(More)
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)