Lower bounds for cutting planes proofs with small coefficients

Publisher： Cambridge University Press

E-ISSN： 1943-5886|62|3|708-728

ISSN： 0022-4812

Source： The Journal of Symbolic Logic, Vol.62, Iss.3, 1997-09, pp. : 708-728

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Abstract

We consider small-weight Cutting Planes (CP*) proofs; that is, Cutting Planes (CP) proofs with coefficients up to Poly(n). We use the well known lower bounds for monotone complexity to prove an exponential lower bound for the length of CP* proofs, for a family of tautologies based on the clique function. Because Resolution is a special case of small-weight CP, our method also gives a new and simpler exponential lower bound for Resolution.

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