arnold beckmann's pages
Separation results for the size of constant-depth propositional proofs
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
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.