Alexander A. Sherstov

Alexander A. Sherstov
SIAM J. Comput.
2011

We develop a novel technique for communication lower bounds, the pattern matrix method. Specifically, fix an arbitrary function f : {0, 1}n → {0, 1} and let Af be the matrix whose columns are each an… (More)

Halfspace Matrices

Alexander A. Sherstov
computational complexity
2007

We introduce the notion of a halfspace matrix, which is a sign matrix A with rows indexed by linear threshold functions f, columns indexed by inputs x ∈ {− 1, 1} n , and the entries given by A f,x =… (More)

Cryptographic Hardness for Learning Intersections of Halfspaces

Adam R. Klivans, Alexander A. Sherstov
2006 47th Annual IEEE Symposium on Foundations of…
2006

We give the first representation-independent hardness results for PAC learning intersections of halfspaces, a central concept class in computational learning theory. Our hardness results are derived… (More)

Separating AC0 from depth-2 majority circuits

We prove that AC<sup>0</sup> cannot be efficiently simulated by MAJºMAJ circuits. Namely, we construct an AC<sup>0</sup> circuit of depth 3 that requires MAJºMAJ circuits of size… (More)

The intersection of two halfspaces has high threshold degree

Alexander A. Sherstov
Electronic Colloquium on Computational Complexity
2009

Function Approximation via Tile Coding: Automating Parameter Choice

Reinforcement learning (RL) is a powerful abstraction of sequential decision making that has an established theoretical foundation and has proven effective in a variety of small, simulated domains.… (More)

The Unbounded-Error Communication Complexity of Symmetric Functions

Alexander A. Sherstov
2008 49th Annual IEEE Symposium on Foundations of…
2008

We prove an essentially tight lower bound on the unbounded-error communication complexity of every symmetric function, i.e.,f(x,y)=D(|x Lambda y|), where D:{0,1,...,n}-rarr{0,1} is a given predicate… (More)

The Communication Complexity of Gap Hamming Distance

Alexander A. Sherstov
Electronic Colloquium on Computational Complexity
2011

In the gap Hamming distance problem, two parties must determine whether their respective strings x,y ∈ {0,1}n are at Hamming distance less than n/2− √ n or greater than n/2+ √ n. In a recent tour de… (More)

The Sign-rank of Ac

The sign-rank of a matrix A = [Aij ] with ±1 entries is the least rank of a real matrix B = [Bij ] with AijBij > 0 for all i, j. We obtain the first exponential lower bound on the sign-rank of a… (More)

Communication Complexity under Product and Nonproduct Distributions

Alexander A. Sherstov
Electronic Colloquium on Computational Complexity
2007

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