2003/08/05 by Russell Impagliazzo, Impagliazzo, Russell, Nathan Segerlind +1
Computer Science · #Advanced Graph Theory Research #Complexity and Algorithms in Graphs #Computational Complexity (cs.CC) #F.4.1 #FOS: Computer and information sciences #Formal Methods in Verification #Logic in Computer Science (cs.LO) #cs.CC #cs.LO
paper · pdf · doi:10.48550/arxiv.cs/0308012
17 pages
arxiv created 2003/08/05 · openalex publication_date 2003/08/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that constant-depth Frege systems with counting axioms modulo m polynomially simulate Nullstellensatz refutations modulo m. Central to this is a new definition of reducibility from formulas to systems of polynomials with the property that, for most previously studied translations of formulas to systems of polynomials, a formula reduces to its translation. When combined with a previous result of the authors, this establishes the first size separation between Nullstellensatz and polynomial calculus refutations. We also obtain new, small refutations for certain CNFs by constant-depth Frege systems with counting axioms.