Browsing by Advisor "Saha, Chandan"
Now showing items 1-7 of 7
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Equivalence test for the trace iterated matrix multiplication polynomial
An m-variate polynomial f is affine equivalent to an n-variate polynomial g if m > n and there is a full rank n * m matrix A and a n-dimensional vector b such that f(x) = g(Ax + b). Given blackbox access to f and g (i.e ... -
Expanders in Arithmetic Circuit Lower Bound : Towards a Separation Between ROABPs and Multilinear Depth 3 Circuits
Consider the problem of Polynomial Identity Testing(PIT): we are given an arithmetic circuit computing a multivariate polynomial over some eld and we have to determine whether that polynomial is identically zero or not. ... -
An Improved Lower Bound for Depth four Arithmetic Circuits
(2018-05-29)We study the problem of proving lower bounds for depth four arithmetic circuits. Depth four circuits have been receiving much attraction when it comes to recent circuit lower bound results, as a result of the series of ... -
An Improved Lower Bound for Multi-r-ic Depth Four Circuits as a Function of the Number of Input Variables
In this work we study the multi-r-ic formula model introduced by [KS15c] and improve upon the lower bound for multi-r-ic depth four circuits given in [KST16b], when viewed as a function of the number of input variables ... -
On Learning and Lower Bound Problems Related to the Iterated Matrix Multiplication Polynomial
The iterated matrix multiplication polynomial (IMM) of width w and length d is the 1x1 entry in the product of d square matrices of size w. The w^2d entries in the d matrices are distinct variables. In this thesis, we study ... -
On symmetries of and equivalence tests for two polynomial families and a circuit class
Two polynomials f, g ∈ F[x1, . . . , xn] over a field F are said to be equivalent if there exists an n×n invertible matrix A over F such that g = f(Ax), where x = (x1 · · · xn)T . The equivalence test (in short, ET) for ... -
Towards a Charcterization of the Symmetries of the Nisan-Wigderson Polynomial Family
(2018-07-09)Understanding the structure and complexity of a polynomial family is a fundamental problem of arithmetic circuit complexity. There are various approaches like studying the lower bounds, which deals with nding the smallest ...