Lower bounds for lovász-schrijver systems and beyond follow from multiparty communication complexity

Authors:
Paul Beame;Toniann Pitassi;Nathan Segerlind
Affiliations:
Computer Science and Engineering, University of Washington, Seattle, WA;Computer Science Department, University of Toronto, Toronto, ON;Computer Science and Engineering, University of Washington, Seattle, WA
Venue:
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Year:
2005

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Abstract

We prove that an ω(log3n) lower bound for the three-party number-on-the-forehead (NOF) communication complexity of the set-disjointness function implies an nω(1) size lower bound for tree-like Lovász-Schrijver systems that refute unsatisfiable CNFs. More generally, we prove that an nΩ(1) lower bound for the (k+1)-party NOF communication complexity of set-disjointness implies a $2^{n^{\Omega(1)}}$ size lower bound for all tree-like proof systems whose formulas are degree k polynomial inequalities.