An Average Case Analysis of Monien and Speckenmeyer's Mechanical Theorem Proving Algorithm

In this paper, we shall give an average case analysis of a mechanical theorem proving algorithin based upon branching techniques for solving the k--satisfiability problem. The branching algorithm is a modified version of Monien and Speckenmeyer's branching algorithm [Monien and Speckenmeyer 1985]. Monien and Speckenmeyer's branching algorithm has a worst case time complexity which is strictly better than 2 n [Monien and Speckenmeyer 1985]. Based upon the probability distribution model that given r clauses, each clause is randomly chosenfrom the set of all k-literal clauses over n variables and each clause is chosen independently with others, we can show that our branching algorithm runs in exponential expected time under the 9 t condition that 11 m ~ ~ | and k is a constant. r,n~ Section