Title: Towards an algebraic natural proofs barrier via polynomial identity testing,
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.