Angewandte Mathematik Und Informatik Universit at Zu K Oln on the Imbalance of Distributions of Solutions of Cnf{formulas and Its Impact on Satissability Solvers Solutions of Cnf{formulas and Its Impact on Satissability Solvers

Let F be Boolean formulas in conjunctive normal form with n variables, r clauses, every clause has length s. We show that if F is split into two subformulas F v and F v by setting v true and false in F , then the expected number of solutions of one of the two subformulas F v and F v is signiicantly higher than that in the other subformula, when dealing with classes of formulas where the great majority of formulas is satissable. We discuss practical consequences of this result.