Abstract:
Decompositions, like Shannon- and Davio-Decomposition are frequently used to design data structures for Boolean functions. There are various ways to expand a Boolean function into three or more subfunctions. This paper introduces decompositions into three and four subfunctions and shows applications in matrix calculus. These decompositions can improve size and processing speed of matrix representations of Boolean functions. It is also shown how to compute canonical matrices. Experiments on Benchmark and random functions are given to verify the feasibility of the method.