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|All Authors / Contributors:||
|Notes:||"January 22, 1991."|
|Description:||11 pages ; 28 cm.|
|Series Title:||Yale University.; Department of Computer Science.; Technical report|
Our oracle is also the first relative to which [formula] is properly contained of [formula], or in the terminology of Wagner's refined polynomial hierarchy , [theta] p/2 is properly contained in [delta] p/2. Our construction depends on a new lower bound for perceptrons, which is interesting in its own right. We construct a predicate that is computable by a small perceptron, but which requires exponentially large weights. This lower bound depends in turn on a fundamental property of polynomials: if p is bounded on the domain [1 ..., m] then the coefficients of p must be small as a function of m."