[Colloquium] THEORY TALK TODAY: Arkadev Chattopadhyay
Katie Casey
caseyk at cs.uchicago.edu
Tue Nov 16 08:31:40 CST 2010
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF CHICAGO
Date: Tuesday, November 16, 2010
Time: 3:00 p.m.
Place: Ryerson 251, 1100 E. 58th Street
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Speaker: Arkadev Chattopadhyay
From: University of Toronto
Web page: http://www.cs.toronto.edu/~arkadev/
Title: Linear systems over arbitrary moduli
Abstract: Consider a system of generalized linear equations over Z_m of the following form: l_i(x_1,...,x_n) in A_i for 1 <= i <= t, where each A_i is a subset of Z_m and m is a constant number like 6. We show that the boolean solution set of such a system has exponentially small correlation with the boolean MOD_q function, if m and q are co-prime. We obtain this result by combining ideas involving matrix rigidity from Grigoriev and Razborov (FOCS 98) with estimates of exponential sums by Bourgain (2005).
This immediately implies that depth-three circuits of type Majority of AND of MOD_m^A need exponential size to compute the MOD_q function. This is the first superpolynomial lower bound on the size of such circuits and settles an open problem due to Beigel and Maciel (Complexity 97).
Based on two works, one joint with Avi Wigderson and the other joint with Shachar Lovett.
Refreshments will be served prior to the talk at 2:30 in Ryerson 255.
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