An open problem in communication complexity proposed by several authors is to prove that for every Boolean function f, the task of computing f(x ∧ y) has polynomially related classical and quantum bounded-error complexities. We solve a variant of this question. For every f, we prove that the task of computing, on input x and y, both of the quantities f(x∧y) and f(x∨y) has polynomially related c...

In 1979 Valiant showed that the complexity class VPe of families with polynomially bounded formula size is contained in the class VPs of families that have algebraic branching programs (ABPs) of polynomially bounded size. Motivated by the problem of separating these classes we study the topological closure VPe, i.e. the class of polynomials that can be approximated arbitrarily closely by polyno...

We construct a framework which allows an algorithm to turn the distributions produced by some boosting algorithms into polynomially smooth distributions (w.r.t. the PAC oracle’s distribution), with minimal performance loss. Further, we explore the case of Freund and Schapire’s AdaBoost algorithm, bounding its distributions to polynomially smooth. The main advantage of AdaBoost over other boosti...

Much work has been done on describing tractable classes of constraint networks. Most of the known tractable examples are described by either restricting the structure of the networks, or their language. Indeed, for both structural or language restrictions very strong dichotomy results have been proven and in both cases it is likely that all practical examples have already been discovered. As su...

Interactive proof systems in which the Prover is restricted to have a polynomial size strategy are investigated. The restriction of polynomial size computation tree, visible to the Prover, or logarithmically bounded number of coin ips by the Veriier guarantee a polynomial size strategy. The additional restriction of logarithmic space is also investigated. A main result of the paper is that inte...

It is proved that for polynomially bounded sets of matrices the notions of pointwise convergence and uniform convergence coincide. This result is also proved for certain sets of nonlinear maps on finite-dimensional real or complex vector spaces.

We establish the homological foundations for studying polynomially bounded group cohomology, and show that the natural map from PH∗(G;Q) to H∗(G;Q) is an isomorphism for a certain class of groups. © 2004 Elsevier B.V. All rights reserved. MSC: 18G10; 18G40; 13D99; 16E30; 20J05; 20F05; 20F65

Let T be an operator-weighted shift whose weights are 2-by-2 matrices. We say that, given > 0, T is in the -canonical form if each weight is an upper triangular matrix (aij), with 0 ≤ a11, a22 ≤ 1 and a12 6= 0 implies a11, a22 < . We generalize this concept to operator-weighted shifts whose weights are n-by-n matrices and we show that every polynomially bounded weighted shift, whose weights are...

The purpose of this article is to present a short model-theoretic proof of the valuation property for a polynomially bounded, o-minimal theory T . The valuation property was conjectured by van den Dries [1], and proved for the polynomially bounded case by van den Dries– Speissegger [4] and for the power bounded case by Tyne [11]. Our proof uses the transfer principle for the theory Tconv (theor...