A Group-Theoretical Approach to Two-Rail Cascades

A two-rail cascade is a one-dimensional binary logic cellular array wherein each noninitial cell has two inputs from the preceding cell and one external input. The initial cell has three external inputs, and the last cell one or two external outputs. The interest in two-rail cascades is due to the fact that one-output two-rail cascades are known to be functionally complete. This paper is concerned with two-output two-rail cascades and derives new synthesis procedures for four and five input variables. These procedures utilize certain properties of the symmetric group of degree 4, as well as known functional decomposition techniques.