The Surprising Power of Constant Depth Algebraic Proofs
Russell Impagliazzo, Sasank Mouli, Toniann Pitassi · 2020
A major open problem in proof complexity is to prove superpolynomial lower bounds for AC0[p]-Frege proofs. This system is the analog of AC0 [p], the class of bounded depth circuits with prime modular counting gates. Despite strong lower bounds for this class dating back thirty years ([28, 30]), there are no significant lower bounds for AC0 [p]-Frege. Significant and extensive degree lower bounds have been obtained for a variety of subsystems of AC0[p]-Frege, including Nullstellensatz ([3]), Polynomial Calculus ([9]), and SOS ([14]). However to date there has been no progress on AC0 [p]-Frege lower bounds.