This paper continued the study of the complexity behavior of the satisfiability analysis of hard random formulas given in the conjunctive normal form (CNF). In the 3-CNF formula, each clause contains three literals of logical variables. The number of logical variables in the formula is N. In this paper, the SAT solver is improved by introducing equality reduction and pure literal identification procedures. The solver improvement reduced the exponent (with base 2) from N/20.86 to N/21.41 with an R=4.6 ratio of the number of clauses to the number of variables. The results show that the efficiency of the pure literals identification procedure decreases as R increases. An important part of the study is an empirical estimation of the algorithmic complexity of the SAT problem with large number of variables. The proposed method gives a convenient lower bound on the complexity of analysis for random 3-CNF formulas. We estimated the algorithmic complexity for the range N=256÷8192. The exponential dependence of complexity on N for random 3-CNF formulas at a fixed value of R is demonstrated in this range.
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
Tel.: +1 703 830 6300
Fax: +1 703 830 2300 email@example.com
(Corporate matters and books only) IOS Press c/o Accucoms US, Inc.
For North America Sales and Customer Service
West Point Commons
Lansdale PA 19446
Tel.: +1 866 855 8967
Fax: +1 215 660 5042 firstname.lastname@example.org