We prove that the Nisan-Wigderson generators based on computationally hard functions and suitable matrices are hard for propositional proof systems that admit feasible interpolation.

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A map $g:\{0,1\}^n\to\{0,1\}^m$ ($m>n$) is a hard proof complexity generator for a proof system $P$ iff for every string $b\in\{0,1\}^m\setminus Rng(g)$, formula $\tau_b(g)$ naturally expressing $b\not\in Rng(g)$ requires superpolynomial size $P$-proofs. One of the well-studied maps in the theory of proof complexity generators is Nisan--Wigderson generator. Razborov (Annals of Mathematics ... more >>>