An exponential lower bound on the length of cutting plane proofs is proved using an extension of a lower bound for monotone circuits to circuits which compute with real numbers and use nondecreasing functions as gates.Expand

It is shown that, for each k, the running time of ResolveSat on a k-CNF formula is significantly better than 2/sup n/, even in the worst case, and the idea of succinctly encoding satisfying solutions can be applied to obtain lower bounds on circuit site.Expand

This basic lemma shows how to encode satisfying solutions of a /spl kappa/-CNF succinctly as well as an upper and lower bound on the size of depth 3 circuits of AND and OR gates computing the parity function.Expand

The problem about the length of proofs of the sentences saying that there is no proof of contradiction in S whose length is < n is considered and the relation of this problem to some problems about propositional proof systems is shown.Expand

Among others, it is proved that the Broken Mosquito Screen pair of disjoint NP sets can be polynomially reduced to Clique–Coloring pair and thus is polynOMially separable and it is shown that the pair ofDisjointNP sets canonically associated with the Resolution proof system is symmetric.Expand

It is shown that nontrivial statements about S2 and its fragments can be derived from this relation, in particular: for i > j ~ 2 the V1:J-consequences if S~ are finitely axiomatizable, which would require proving superpolynomial lower bounds to the length of proofs in proof systems G.Expand