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On the Asymptotic Nullstellensatz and Polynomial Calculus Proof Complexity

2008
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Logic in Computer Science
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We show that the asymptotic complexity of uniformly generated (expressible in First-Order (FO) logic) propositional tautologies for the Nullstellensatz proof system (NS) as well as for Polynomial Calculus, (PC) has four distinct types of asymptotic behavior over fields of finite characteristic. More precisely, based on some highly non-trivial work by Krajicek, we show that for each prime p there exists a function l(n) ∈ Ω(log(n)) for NS and l(n) ∈ Ω(log(log(n)) for PC, such that the

doi:10.1109/lics.2008.30
dblp:conf/lics/Riis08
fatcat:hij6dbovtvgirjnlph24ztbifu