Journal of Symbolic Logic

Lower Bounds for Cutting Planes Proofs with Small Coefficients

Maria Bonet, Toniann Pitassi, and Ran Raz

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.

Abstract

We consider small-weight Cutting Planes $(\mathrm{CP}^\ast)$ proofs; that is, Cutting Planes (CP) proofs with coefficients up to $\operatorname{Poly}(n)$. We use the well known lower bounds for monotone complexity to prove an exponential lower bound for the length of $\mathrm{CP}^\ast$ 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. We also prove the following two theorems: (1) Tree-like $\mathrm{CP}^\ast$ proofs cannot polynomially simulate non-tree-like $\mathrm{CP}^\ast$ proofs. (2) Tree-like $(\mathrm{CP}^\ast$ proofs and Bounded-depth-Frege proofs cannot polynomially simulate each other. Our proofs also work for some generalizations of the $\mathrm{CP}^\ast$ proof system. In particular, they work for $\mathrm{CP}^\ast$ with a deduction rule, and also for any proof system that allows any formula with small communication complexity, and any set of sound rules of inference.

Article information

Source
J. Symbolic Logic, Volume 62, Issue 3 (1997), 708-728.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745294

Mathematical Reviews number (MathSciNet)
MR1472120

Zentralblatt MATH identifier
0889.03050

JSTOR
links.jstor.org

Citation

Bonet, Maria; Pitassi, Toniann; Raz, Ran. Lower Bounds for Cutting Planes Proofs with Small Coefficients. J. Symbolic Logic 62 (1997), no. 3, 708--728. https://projecteuclid.org/euclid.jsl/1183745294


Export citation