Deciding Satisfiability in the Twinkling of an Eye

Abstract

The question as to whether a CNF Boolean formula is satisfiable is referred to as Boolean satisfiability problem (SAT). For decades now, this problem has attracted a great deal of attention. A well-known algorithm for solving this problem is the DPLL algorithm. However, this algorithm may run in an exponential (long) time. The great plan embraced in this work is to show how the satisfiability of any CNF Boolean formula can be decided in a very short time. This is achieved by the modification of the DPLL algorithm and the introduction of a quick algorithm.