Complexity of Semi-algebraic Proofs

@article{Grigoriev2001ComplexityOS,
  title={Complexity of Semi-algebraic Proofs},
  author={Dima Grigoriev and Edward A. Hirsch and Dmitrii V. Pasechnik},
  journal={Electronic Colloquium on Computational Complexity (ECCC)},
  year={2001}
}
Proof systems for polynomial inequalities in 0-1 variables include the well-studied Cutting Planes proof system (CP) and the LovászSchrijver calculi (LS) utilizing linear, respectively, quadratic, inequalities. We introduce generalizations LS of LS involving polynomial inequalities of degree at most d. Surprisingly, the systems LS turn out to be very strong. We construct polynomial-size bounded degree LS proofs of the clique-coloring tautologies (which have no polynomial-size CP proofs), the… CONTINUE READING
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Complexity of semi-algebraic proofs

  • D. Grigoriev, E. A. Hirsch, D. V. Pasechnik
  • Technical report, Electronic Colloquim on…
  • 2001
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