A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function and connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy.Expand

It is proved that an algorithm due to Kushilevitz and Mansour can be used to weakly learn DNF using membership queries in polynomial time, with respect to the uniform distribution on the inputs, and it is obtained that DNF expressions and decision trees are not evenWeakly learnable with any unproven assumptions.Expand

A new model is studied, in which a collection of processes P0, ..., Pk−1 that share information about a set of integers {a0, …,ak−1}, communicate to determine a 0-1 predicate of the numbers.Expand

This paper shows how to construct several cryptographic primitives based on certain assumptions on the difficulty of learning by developing further a line of thought introduced by Impagliazzo and Levin.Expand

It is demonstrated that the normal closure of a subgroup can be computed in polynomial time, and that this proceaure can be used to test a group for solvability.Expand

We show that any group represented by generators that are cycles of bounded degree has O(n2) diameter, i.e., that the longest product of generators required to reach any permutation in the group is… Expand

The first correct proof that, for a random oracleA, PPA is properly contained in PSPACEA is given, which allows the new result that an AC0 circuit with one majority gate cannot approximate parity to be proved.Expand

An entirely different viewpoint is presented in which one seeks distributional information about the huge family of all cellular imbeddings of a graph into all closed surfaces, instead of focusing on just one imbedding or on the existence of imbedDings into just one surface.Expand

Topological methods and a reduction to linear matroid parity are used to develop a polynomial-time algorithm to find a maximum-genus cellular imbedding, which seems to be the first im Bedding algorithm for which the running time is not exponential in the genus of the imbeding surface.Expand