Computation of Disjoint Cube Representations Using a Maximal Binate Variable Heuristic ∗

A method for computing the Disjoint-Sum-Of-Products (DSOP) form of Boolean functions is described. The algorithm exploits the property of the most binate variable in a set of cubes to compute a DSOP form. The technique uses a minimized Sum-Of-Products (SOP) cube list as input. Experimental results comparing the size of the DSOP cube list produced by this algorithm and those produced by other methods demonstrate the efficiency of this technique and show that superior results occur in many cases for a set of benchmark functions. I. INTRODUCTION Representing a Boolean function in the form of a Disjoint-Sum-Of-Products (DSOP) cube list has many advantages in Computer Aided Design (CAD) tools. DSOPs can be used to efficiently compute the spectra of Boolean functions [3,4,8], in the minimization of Exclusive-OR-Sum-of-Products (ESOPs) [5,9,10,11] and to quickly find the complement of Boolean functions [6]. This fact has encouraged researchers to invent new algorithms [1,2] to generate the DSOP forms of Boolean functions efficiently. Given a logic function in the form of a minimized Sum-Of-Products (SOP) cube list, the algorithm presented here computes the corresponding DSOP form by splitting the SOP cube list according to the variable that occurs most often in both the complemented and uncomplemented form. The two resulting cube lists represent Shannon cofactor functions about the splitting variable. The motivating paradigm of this technique is to attempt to produce cofactor cube lists that contain roughly an equal number of supporting minterms. Choosing the variable that exists in complemented and uncomplemented forms equally in a minimized SOP cube list corresponds to choosing the " most binate " variable of the subfunction. By choosing such a variable about which to decompose the function is likely to yield cofactor functions of approximately equally complex functions in terms of supporting minterm counts.