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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > DEPTH THREE CIRCUITS:
Reports tagged with depth three circuits:
TR15-154 | 22nd September 2015
Neeraj Kayal, Vineet Nair, Chandan Saha

Separation between Read-once Oblivious Algebraic Branching Programs (ROABPs) and Multilinear Depth Three Circuits

We show an exponential separation between two well-studied models of algebraic computation, namely read-once oblivious algebraic branching programs (ROABPs) and multilinear depth three circuits. In particular we show the following:

1. There exists an explicit n-variate polynomial computable by linear sized multilinear depth three circuits (with only two product gates) ... more >>>


TR16-187 | 21st November 2016
morris yau

Almost Cubic Bound for Depth Three Circuits in VP

Revisions: 3

In "An Almost Cubic Lower Bound for \sum\prod\sum circuits in VP", [BLS16] present an infinite family of polynomials, \{P_n\}_{n \in \mathbb{Z}^+}, with P_n
on N = \Theta(n polylog(n))
variables with degree N being in VP such that every
\sum\prod\sum circuit computing P_n is of size \Omega\big(\frac{N^3}{2^{\sqrt{\log N}}}\big).
We ... more >>>




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