Methods of decomposition of Boolean functions

Abstract

The article considers on of the main types of Boolean functions conversion – their decomposition. The decomposition is being used in many applications for studying and designing complex objects and systems with logical methods. Firstly, the article observes decomposition of Boolean functions represented in the truth table. Among traditional decomposition approaches, the article describes formulas presented by Boole and Shannon and special methods of orthonormal expansions. Then, the paper considers contemporary decomposition techniques and their classification. Next, the article discusses representation of Boolean functions in normal forms and essential features of that representation, important for decomposition. After that, the article reviews decomposition techniques for boolean functions represented in conjunctive normal forms (CNF). The study mentions CNF partitioning as hypergraph partitioning. Then the paper discusses applications generating large CNFs. Minimization of large CNFs with traditional methods is impossible. Their minimization is possible only using decomposition techniques. The separate class of tasks is minimization of Horn formulas. Finally, at the conclusion, the study discusses decomposition for parallelization of SAT problem.