Computation of Prime Implicants Using Matrix and Paths

In this paper, an efficient algorithm to compute the set of prime implicants of a prepositional formula in Conjunc-tive Normal Form (CNF) is presented. The proposed algorithm uses a concept of representing the formula as a bi-nary matrix and computing paths through the matrix as implicants. The algorithm finds the prime implicants as theprime paths using the divide-and-conquer technique. The proposed algorithm can be used for knowledge compila-tion, Clause Maintenance Systems where the knowledge base is prepositional formulae. Moreover, the algorithm iseasily adaptable to the incremental mode of computation where an earlier formula is updated by a set of clauses.