Elimination of Infrequent Variables Improves Average Case Performance of Satisfiability Algorithms

Preprocessing a random instance I of CNF Satisfiability in order to remove infrequent variables (those which appear once or twice in an instance) from I is considered. The model used to generate random instances is the popular random-clause-size model with parameters n; the number of clauses, r; the number of Boolean variables from which clauses are composed; and p, the probability that a variable appears in a clause as a positive (or negative) literal. It is shown that exhaustive search over such preprocessed instances runs in polynomial average time over a significantly larger parameter space than has been shown for any other algorithm under the random-clause-size model when $n = r^\epsilon ,\epsilon \epsilon > 0$, and $pr \epsilon \geqslant \frac{2}{3...