 
Summary: Satisability, Branchwidth and Tseitin
Tautologies
Michael Alekhnovich Alexander A. Razborov y
September 12, 2002
Abstract
For a CNF , let w b () be the branchwidth of its underlying hy
pergraph. In this paper we design an algorithm for solving SAT in
time n O(1) 2 O(w b ()) . This in particular implies a polynomial algorithm
for testing satisability on instances with treewidth O(log n).
Our algorithm is a modication of the width based automated the
orem prover (WBATP) which is a popular (at least on the theoretical
level) heuristic for nding resolution refutations of unsatisable CNFs.
We show that instead of the exhaustive enumeration of all provable
clauses, one can do a better search based on the RobertsonSeymour
algorithm for approximating the branchwidth of a graph. We call the
resulting procedure BranchWidth Based Automated Theorem Prover
(BWBATP). As opposed to WBATP, it always produces regular refu
tations. Perhaps more importantly, the running time of our algorithm
is bounded in terms of a clean combinatorial characteristic that can be
eÆciently approximated, and that the algorithm also produces, within
