An Incremental Method for Generating Prime Implicants/Impicates

Given the recent investigation of Clause Management Systems (CMSs) for Artificial Intelligence applications, there is an urgent need for art efficient incremental method for generating prime implicants. Given a set of clauses 5 c, a set of prime implicants 1I of ~ and a clause C, the problem can be formulated as finding the set of prime implicaate for II t.J {C). Intuitively, the property of implicants being prime implies that any effort to generate prime implicants from a set of prime implica~ts will not yield any new prime implicants but themselves. In this paper, we exploit the properties of prime implicaats and propose an inerementM method for generating prime implicants from a set of existing prime implieants plus a new clause. The correctness proof and complexity analysis of the incremental method are presented, and the intricacy of subsumptions in the incremental method is also examined. Additionally, the role of prime implicants in the CMS is also mentioned.