Shared multiple-valued decision diagrams for multiple-output functions

In this paper, we propose a method to represent multiple-output functions using shared multiple-valued decision diagrams (SMDDs). We show an algorithm for pairing the input variables of binary decision diagrams (BDDs). We also present the pair sifting that moves pairs of 4-valued input variables to speed up the normal sifting, and to produce compact SMDDs. The size of the SMDD is the total number of non-terminal nodes excluding the nodes for output selection variables. We derive the sizes of SMDDs for general functions and symmetric functions. From experimental results, we conjecture that, for n > 1, the sizes of SMDDs for bit-counting functions (wgt n) and incrementing functions line n) are n[log(2) n] + n - 2([log2 n]) and 2n - 1, respectively, where n is the number of binary input variables, and [a] denotes the largest integer not greater than a. We also compare our method with other one. Experimental results show the efficiency of our method.