Majority Logic Representation and Satisfiability

Majority logic is a powerful generalization of common AND/OR logic. Original two-level and multi-level logic networks can use majority operators as primitive connective, in place of AND/ORs. In such a way, Boolean functions have novel means for compact representation and efficient manipulation. In this paper, we focus on two-level logic representation. We define a Majority Normal Form (MNF), as an alternative to traditional Disjunctive Normal Form (DNF) and Conjunctive Normal Form (CNF). After a brief investigation on the MNF expressive power, we study the problem of MNF-SATisfiability (MNF-SAT). We prove that MNF-SAT is NP-complete, as its CNF-SAT counterpart. However, we show practical restrictions on MNF formula whose satisfiability can be decided in polynomial time. We finally propose a simple algorithm to solve MNF- SAT, based on the intrinsic functionality of two-level majority logic. Although an automated MNF-SAT solver is still under construction, manual examples already demonstrate promising opportunities.