Towards an algebraic natural proofs barrier via polynomial identity testing [article]

Joshua A. Grochow and Mrinal Kumar and Michael Saks and Shubhangi Saraf
2017 arXiv   pre-print
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
more » ... rier, geometric complexity theory, and (algebraic) proof complexity.
arXiv:1701.01717v1 fatcat:tfx54wjxcrdlpkm4kdkou3qthm