PIT for depth-$4$ circuits and Sylvester-Gallai conjecture for polynomials
Abstract
This text is a development of a preprint of Ankit Gupta. We present an approach for devising a deterministic polynomial time blackbox identity testing (PIT) algorithm for depth- circuits with bounded top fanin. This approach is similar to Kayal-Shubhangi approach for depth- circuits. Kayal and Shubhangi based their algorithm on Sylvester-Gallai-type theorem about linear polynomials. We show how it is possible to generalize this approach to depth- circuits. However we failed to implement this plan completely. We succeeded to construct a polynomial time deterministic algorithm for depth- circuits with bounded top fanin and its correctness requires a hypothesis. Also we present a polynomial-time (unconditional) algorithm for some subclass of depth- circuits with bounded top fanin.
Cite
@article{arxiv.1902.07201,
title = {PIT for depth-$4$ circuits and Sylvester-Gallai conjecture for polynomials},
author = {Alexey Milovanov},
journal= {arXiv preprint arXiv:1902.07201},
year = {2019}
}
Comments
12 pages