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The Relation between Polynomial Calculus, Sherali-Adams, and Sum-of-Squares Proofs Berkholz, Christoph Proof Complexity Polynomial Calculus Sum-of-Squares Sherali-Adams We relate different approaches for proving the unsatisfiability of a system of real polynomial equations over Boolean variables. On the one hand, there are the static proof systems Sherali-Adams and sum-of-squares (a.k.a. Lasserre), which are based on linear and semi-definite programming relaxations. On the other hand, we consider polynomial calculus, which is a dynamic algebraic proof system that models Gröbner basis computations. Our first result is that sum-of-squares simulates polynomial calculus: any polynomial calculus refutation of degree d can be transformed into a sum-of-squares refutation of degree 2d and only polynomial increase in size. In contrast, our second result shows that this is not the case for Sherali-Adams: there are systems of polynomial equations that have polynomial calculus refutations of degree 3 and polynomial size, but require Sherali-Adams refutations of large degree and exponential size. A corollary of our first result is that the proof systems Positivstellensatz and Positivstellensatz Calculus, which have been separated over non-Boolean polynomials, simulate each other in the presence of Boolean axioms. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Christoph Berkholz 2018 Is Part Of LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2018.11 urn:nbn:de:0030-drops-85279 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.11 eng https://creativecommons.org/licenses/by/3.0/legalcode