Towards an algebraic natural proofs barrier via polynomial identity testing
Computational Complexity
2017-01-09 v1 Algebraic Geometry
Abstract
We observe that a certain kind of algebraic proof - which covers essentially all known algebraic circuit lower bounds to date - cannot be used to prove lower bounds against VP if and only if what we call succinct hitting sets exist for VP. This is analogous to the Razborov-Rudich natural proofs barrier in Boolean circuit complexity, in that we rule out a large class of lower bound techniques under a derandomization assumption. We also discuss connections between this algebraic natural proofs barrier, geometric complexity theory, and (algebraic) proof complexity.
Keywords
Cite
@article{arxiv.1701.01717,
title = {Towards an algebraic natural proofs barrier via polynomial identity testing},
author = {Joshua A. Grochow and Mrinal Kumar and Michael Saks and Shubhangi Saraf},
journal= {arXiv preprint arXiv:1701.01717},
year = {2017}
}