Recursive optimization on converting CNF to DNF using grid computing

Abstract

A NP hard problem CNF to DNF conversion is a vast area of research for AI, circuit design, FPGA’s (Miltersen et al. in On converting CNF To DNF, 2003), PLA’s, etc. (Beame in A switching lemma primer, 1994; Kottler and Kaufmann in SArTagnan—a parallel portfolio SAT solver with lockless physical clause sharing, 2011). Optimization and its statistics has become a potential requirement for analysis and behavior of normal form conversion. Various applications are in its requirement like gnome analysis, grid computing, bioinformatics, imaging systems, rough sets require higher variable processing algorithm. Problem statement is—design and implementation of optimal conjunctive normal form to optimal (prime implicants) disjunctive normal form conversion which is an “NP hard problem conversion to an NP complete”. Thus CNF to DNF can only be considered to evaluate best performance for higher variable processing on high end systems. The best-known representations of Boolean functions f are those as disjunctions of terms (DNFs) and as conjunctions of clauses (CNFs) (Beame 1994; Kottler and Kaufmann 2011) (Wegener in The complexity of boolean functions, 1987). It is convenient to define the DNF size of f as the minimal number of terms in a DNF representing f and the CNF size as the minimal number of clauses in a CNF representing f (Kottler and Kaufmann 2011).