Lower Bounds for Lovász-Schrijver Systems and Beyond Follow from Multiparty Communication Complexity

  • Paul Beame
  • Toniann Pitassi
  • Nathan Segerlind
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3580)


We prove that an ω(log3 n) lower bound for the three-party number-on-the-forehead (NOF) communication complexity of the set-disjointness function implies an n ω(1) size lower bound for tree-like Lovász-Schrijver systems that refute unsatisfiable CNFs. More generally, we prove that an n Ω(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.


Communication Complexity Proof System Charge Vector Discrete Apply Mathematic Polynomial Inequality 
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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Paul Beame
    • 1
  • Toniann Pitassi
    • 2
  • Nathan Segerlind
    • 1
  1. 1.Computer Science and EngineeringUniversity of WashingtonSeattle
  2. 2.Computer Science DepartmentUniversity of TorontoToronto

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