arnold beckmann's pages

Separation results for the size of constant-depth propositional proofs

File: PDF-File

Author: Arnold Beckmann and Sam Buss
Title: Separation results for the size of constant-depth propositional proofs
Journal: Annals of Pure and Applied Logic 2005, 136: 30-55
Festschrift on the occasion of Wolfram Pohlers' 60th birthday
DOI: 10.1016/j.apal.2005.05.002

Abstract: This paper proves exponential separations between depth d-LK and depth (d+1/2)-LK for every d in 0, 1/2, 1, 1 1/2,... utilizing the order induction principle. As a consequence, we obtain an exponential separation between depth d-LK and depth (d+1)-LK for d in 0,1,2,... . We investigate the relationship between the sequence-size, tree-size and height of depth d-LK-derivations for d in 0, 1/2, 1, 1 1/2,... and describe transformations between them.

We define a general method to lift principles requiring exponential tree-size (d+1/2)-LK-refutations for d in 0,1,2,... to principles requiring exponential sequence-size d-LK-refutations, which will be described for the Ramsey principle and d=0. From this we also deduce width lower bounds for resolution refutations of the Ramsey principle.

websites: Arnold Beckmann 2017-08-28 Valid HTML 4.01! Valid CSS!