Complexity of Semialgebraic Proofs

Complexity of Semialgebraic Proofs with Restricted Degree of Falsity

A weakened version of the Cutting Plane (CP) proof system with a restriction on the degree of falsity of intermediate inequalities was introduced by Goerdt. He proved an exponential lower bound for CP proofs with degree of falsity bounded by n log2 n+1 , where n is the number of variables. Hirsch and Nikolenko strengthened this result by establishing a direct connection between CP and Resolutio...

Semialgebraic complexity of functions

In this paper we study the rate of the best approximation of a given function by semialgebraic functions of a prescribed ‘‘combinatorial complexity’’. We call this rate a ‘‘Semialgebraic Complexity’’ of the approximated function. By the classical Approximation Theory, the rate of a polynomial approximation is determined by the regularity of the approximated function (the number of its continuou...

On the Width of Semialgebraic Proofs and Algorithms

In this paper we study width of semi-algebraic proof systems and various cut-based procedures in integer programming. We focus on two important systems: Gomory-Chvátal cutting planes and LovászSchrijver lift-and-project procedures. We develop general methods for proving width lower bounds and apply them to random k-CNFs and several popular combinatorial principles like the perfect matching prin...

Complexity of Propositional Proofs

The Complexity of Propositional Proofs

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