Analyzing Decompositions of a System of Boolean Functions Using the Ternary Matrix Cover Approach

Subject Areas : B. Computer Systems Organization

Saeid Taghavi Afshord ¹ , Yuri Pottosin ²

1 - Computer EngineeringDepartment, Shabestar Branch, Islamic Azad University, Shabestar, Iran
2 - United Institute of Engineering Cybernetics, National Academy of Sciences of Belarus,Minsk, Belarus

Received: 2013-09-18 Accepted : 2013-09-18 Published : 2013-05-01

Keywords: Boolean functions, Decomposition, Cover map, Compact table, Logic synthesis,

Abstract :

The problem of series two-block disjoint decomposition of completely specified Boolean functions is considered. Analysis and investigation of such systems are very important in logical design context. Recently, a good method for solving this problem was suggested which has been based on the ternary matrix cover approach. Using this method a computer program was developed. This paper is focused on decomposability of a system of Boolean functions. The experiments were done on generated systems and standard benchmarks. In decomposable systems, the total number of solutions and the time elapsed to achieve them are inspected. The total number of solutions among all partitions for investigated systems, ranged between 3% and 87% in generated systems and also, 1% and 96% in standard benchmarks.