Grochow and Pitassi (2018) introduced the algebraic proof system, the Ideal Proof System (IPS), which connects algebraic circuit complexity to propositional proof complexity. They showed that propositional proof systems such as Extended Frege (Frege) are equivalent to circuit IPS (formula IPS) if the correctness of PIT for circuits (formulas) can ... more >>>

We give new lower bounds for the fragments of the Ideal Proof System (IPS) introduced by Grochow and Pitassi (JACM 2018). The Ideal Proof System is a central topic in algebraic proof complexity developed in the context of Nullstellensatz refutation (Beame, Impagliazzo, Krajicek, Pitassi, Pudlak, FOCS 1994) and simulates Extended ... more >>>

We establish an $\epsilon$-sensitive hierarchy separation for monotone arithmetic computations. The notion of $\epsilon$-sensitive monotone lower bounds was recently introduced by Hrubes [Computational Complexity'20]. We show the following:

(1) There exists a monotone polynomial over $n$ variables in VNP that cannot be computed by $2^{o(n)}$ size monotone ... more >>>