Improved lower bounds for tree-like resolution over linear inequalities

Authors:
Arist Kojevnikov
Affiliations:
St.Petersburg Department of Steklov Institute of Mathematics, St.Petersburg, Russia
Venue:
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Year:
2007

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Abstract

We continue a study initiated by Krajíček of a Resolution-like proof system working with clauses of linear inequalities, R(CP). For all proof systems of this kind Krajíček proved in [1] an exponential lower bound of the form: exp(nΩ(1))/MO(W log2 n), where M is the maximal absolute value of coefficients in a given proof and W is the maximal clause width. In this paper we improve this lower bound. For tree-like R(CP)-like proof systems we remove a dependence on the maximal absolute value of coefficients M, hence, we give the answer to an open question from [2]. Proof follows from an upper bound on the real communication complexity of a polyhedra.