On Decomposing Systems of Boolean Functions via Ternary Matrix Cover Approach

The problem of two-block disjoint decomposition of completely specified Boolean functions is considered. Recently a good method in functional decomposition category was proposed. This method is based on using the ternary matrix cover approach. Due to investigation and analysis of this method and to search for an appropriate partition, a computer program was developed. After running the program on thousands of systems of Boolean functions, experimental results show that more than 95% of the inspected systems are decomposable. To obtain a solution of the task in decomposable systems, an efficient technique is also proposed. Using this technique, investigation of one partition was enough to determine decomposability of the inspected systems.