Towards an algebraic natural proofs barrier via polynomial identity testing

Joshua A. Grochow; Mrinal Kumar; Michael Saks; Shubhangi Saraf

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arXiv · 1701.01717

Towards an algebraic natural proofs barrier via polynomial identity testing

Joshua A. Grochow·Mrinal Kumar·Michael Saks·Shubhangi Saraf

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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.

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Joshua A. Grochow, Mrinal Kumar, Michael Saks, Shubhangi Saraf. 2017-01-06. Towards an algebraic natural proofs barrier via polynomial identity testing. https://arxiv.org/abs/1701.01717

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