Towards an algebraic natural proofs barrier via polynomial identity testing

Electronic Colloquium on Computational Complexity (ECCC), Volume abs/1701.01717, 2017.

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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 th...More



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