Number of models and satisfiability of sets of clauses

AbstractWe present a way of calculating the number of models of propositional formulas represented by sets of clauses. The complexity of such a procedure is O(ψnk), where k is the length of clauses and n is the number of variables in the clauses. The value of ψ2 is approximately 1.619, value of ψ3 is approximately 1.840 and the value of ψk approaches 2 when k is large. Further we apply the theory on satisfiability problems, especially on the 3-SAT problems. The complexity of the 3-SAT problems is O(ψn), where n is the number of variables in the clauses. The value of ψ is approximately 1.571 which is better than the results in Schiermeyer (1993) and Monien and Schiermeyer (1985)