On non-canonical solving the Satisfiability problem

Abstract

We study the non-canonical method for solving the Satisfiability problem which given by a formula in the form of the conjunctive normal form. The essence of this method consists in counting the number of tuples of Boolean variables, on which at least one clause of the given formula is false. On this basis the solution of the problem obtains in the form YES or NO without constructing tuple, when the answer is YES. It is found that if the clause in the given formula has pairwise contrary literals, then the problem can be solved efficiently. However, when in the formula there are a long chain of clauses with pairwise non-contrary literals, the solution leads to an exponential calculations.