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We observe that a certain kind of algebraic proof - which covers essentiallyall known algebraic circuit lower bounds to date - cannot be used to provelower bounds against VP if and only if what we call succinct hitting sets existfor VP. This is analogous to the Razborov-Rudich natural proofs barrier inBoolean circuit complexity, in that we rule out a large class of lower boundtechniques under a derandomization assumption. We also discuss connectionsbetween this algebraic natural proofs barrier, geometric complexity theory, and(algebraic) proof complexity.

Towards an algebraic natural proofs barrier via polynomial identity testing