Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10331046 | Information Processing Letters | 2016 | 4 Pages |
Abstract
In this note, we show that over fields of any characteristic, exponential sums of Boolean instantiations of polynomials computed by multilinear circuits can be computed by multilinear circuits with polynomial blow-up in size. In particular, multilinear-VNP equals multilinear-VP. Our result showing closure under exponential sums also holds for other restricted multilinear classes - polynomials computed by multilinear (bounded-width) algebraic branching programs and formulas. Furthermore, it holds even if the circuit class is not fully multilinear but computes a polynomial that is multilinear in the summation variables.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Meena Mahajan, Nitin Saurabh, Sébastien Tavenas,