Abstract
In this chapter, we focus on a novel two-level logic representation. We define Majority Normal Form (MNF), as an alternative to the traditional Disjunctive Normal Form (DNF) and the 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.
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Notes
- 1.
The tautology check problem has been introduced in Chap. 4 of this book.
- 2.
The final majority operator in an MNF is the one in the top layer of the two-level representation form, thus computing the output MNF function.
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Amaru, L.G. (2017). Majority Normal Form Representation and Satisfiability. In: New Data Structures and Algorithms for Logic Synthesis and Verification. Springer, Cham. https://doi.org/10.1007/978-3-319-43174-1_5
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DOI: https://doi.org/10.1007/978-3-319-43174-1_5
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