Kayal, Neeraj and Saha, Chandan and Tavenas, Sebastien (2018) On the Size of Homogeneous and of DepthFour Formulas with Low Individual Degree. In: THEORY OF COMPUTING, 14 .

PDF
The_Com_1416_2018.pdf  Published Version Download (439kB)  Preview 
Abstract
Let r >= 1 be an integer. Let us call a polynomial f (x(1), x(2),..., x(N)) is an element of Fx] a multiric polynomial if the degree of f with respect to any variable is at most r. (This generalizes the notion of multilinear polynomials.) We investigate the arithmetic circuits in which the output is syntactically forced to be a multiric polynomial and refer to these as multiric circuits. We prove lower bounds for several subclasses of such circuits, including the following. 1. An NOmega((logN)) lower bound against homogeneous multiric formulas ( for an explicit multiric polynomial on N variables). 2. An (n/r(1.1))(Omega)((root d/r)) lower bound against depthfour multiric circuits computing the polynomial IMMn,d corresponding to the product of d matrices of size n x n each. 3. A 2(Omega)((root N)) lower bound against depthfour multiric circuits computing an explicit multiric polynomial on N variables.
Item Type:  Journal Article 

Additional Information:  Copyright of this article belongs to UNIV CHICAGO, DEPT COMPUTER SCIENCE 
Keywords:  complexity theory; lower bounds; algebraic complexity; arithmetic formulas; arithmetic circuits; partial derivatives 
Department/Centre:  Division of Electrical Sciences > Computer Science & Automation 
Depositing User:  Francis Jayakanth 
Date Deposited:  10 Feb 2019 09:42 
Last Modified:  10 Feb 2019 09:42 
URI:  http://eprints.iisc.ac.in/id/eprint/61361 
Actions (login required)
View Item 