TR17-009 Authors: Joshua Grochow, Mrinal Kumar, Michael Saks, Shubhangi Saraf

Publication: 22nd January 2017 14:59

Downloads: 423

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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 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.