Kayal, N and Saha, C and Tavenas, S (2018) On the size of homogeneous and of depthfour formulas with low individual degree. In: Theory of Computing, 14 .

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Abstract
Let r â�¥ 1 be an integer. Let us call a polynomial f (x 1 , x 2 , â�¦, x N ) â�� 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 N Î©(logN) lower bound against homogeneous multiric formulas (for an explicit multiric polynomial ( â�� ) on N variables). 2. An (n/r 1.1 ) Î©d/r lower bound against depthfour multiric circuits computing the polynomial IMM n,d corresponding to the product of d matrices of size n Ã� n each. Â© 2018 Neerak Kayal, Chandan Saha, and SÃ©bastien Tavenas.
Item Type:  Journal Article 

Publication:  Theory of Computing 
Publisher:  University of Chicago, Department of Computer Science 
Additional Information:  Copyright for this article belongs to 
Department/Centre:  Division of Electrical Sciences > Computer Science & Automation 
Date Deposited:  20 Mar 2019 05:54 
Last Modified:  20 Mar 2019 05:54 
URI:  http://eprints.iisc.ac.in/id/eprint/62047 
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