On the Relative Complexity of Resolution Refinements and Cutting Planes Proof Systems

Maria Luisa Bonet, Juan Luis Esteban, Nicola Galesi, Jan Johannsen
2000 SIAM journal on computing (Print)  
An exponential lower bound for the size of tree-like cutting planes refutations of a certain family of conjunctive normal form (CNF) formulas with polynomial size resolution refutations is proved. This implies an exponential separation between the tree-like versions and the dag-like versions of resolution and cutting planes. In both cases only superpolynomial separations were known [In order to prove these separations, the lower bounds on the depth of monotone circuits of Raz and McKenzie in
more » ... mbinatorica, 19 (1999), pp. 403-435] are extended to monotone real circuits. An exponential separation is also proved between tree-like resolution and several refinements of resolution: negative resolution and regular resolution. Actually, this last separation also provides a separation between tree-like resolution and ordered resolution, and thus the corresponding superpolynomial separation of [A. Urquhart, Bull. Symbolic Logic, 1 (1995), pp. 425-467] is extended. Finally, an exponential separation between ordered resolution and unrestricted resolution (also negative resolution) is proved. Only a superpolynomial separation between ordered and unrestricted resolution was previously known [
doi:10.1137/s0097539799352474 fatcat:xiyrppe6vvc6zakntfetsrjcdu