Scaling properties of pure random walk on random 3-SAT

Abstract

Experimental results are given on the scaling of the Pure Random Walk version (PRWSAT) of WalkSAT. PRWSAT is very simple because of the absence of heuristics: not only the clause is selected at random, but also the literal within that clause. The main resultis that, despite the simplicity and absence of heuristics, it has non trivial behavior on Random 3-SAT. There appears to be a threshold at a clause/variable ratio of about 2.65. Below the threshold, problems care solved in a tightly-distributed and linear number of flips. Above the threshold scaling appears to be non-polynomial. The simplicity and the nontrivial threshold make it a good candidate for theoretical analysis.