Bounded-Depth Frege with Counting Principles Polynomially Simulates Nullstellensatz Refutations

Russell Impagliazzo and Nathan Segerlind
November 14, 2001

We show that bounded-depth Frege systems with counting principles modulo m can polynomially simulate Nullstellensatz refutations modulo m. This establishes new upper bounds for proofs of certain tautologies in bounded-depth Frege with counting axioms systems. When combined with another result of the authors, this simulation establishes a size (as opposed to a degree) separation between Nullstellensatz and polynomial calculus refutations.

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