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Summary: Satis ability, Branch-width and Tseitin
Tautologies
Michael Alekhnovich Alexander A. Razborov y
September 12, 2002
Abstract
For a CNF , let w b ( ) be the branch-width 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 satis ability on instances with tree-width O(log n).
Our algorithm is a modi cation 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 unsatis able CNFs.
We show that instead of the exhaustive enumeration of all provable
clauses, one can do a better search based on the Robertson-Seymour
algorithm for approximating the branch-width of a graph. We call the
resulting procedure Branch-Width 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
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