An Exact and a Randomized Approach for the Satisfiability Problem

In this paper, three simple algorithms for the satisfiability problem are presented with their probabilistic analyses. One algorithm, called counting, is designed to enumerate all the solutions of an instance of satisfiability. The second one, namely E-SAT, is proposed for solving the corresponding decision problem. Both the enumeration and decision algorithms have a linear space complexity and a polynomial average time performance for a specified class of instances. The third algorithm is a randomized variant of E-SAT. Its probabilistic analysis yields a polynomial average time performance.