Upper and lower bounds for tree-like cutting planes proofs

Abstract

We study the complexity of cutting planes (CP) refutations, and tree-like CP refutations. Tree-like CP proofs are natural and still quite powerful. In particular, the propositional pigeonhole principle (PHP) has been shown to have polynomial-sized tree-like CP proofs. Our main result shows that a family of tautologies, introduced in this paper requires exponential-sized tree-like CP proofs. We obtain this result by introducing a new method which relates the size of a CP refutation to the communication complexity of a related search problem. Because these tautologies have polynomial-sized Frege proofs, it follows that tree-like CP cannot polynomially simulate Frege systems.< >