Representations of multiple-output switching functions using multiple-valued pseudo-Kronecker decision diagrams

Abstract

In this paper, we propose a method to construct smaller multiple-valued pseudo-Kronecker decision diagrams (MVPKDDs). Our method first generates a 4-valued input 2-valued multiple-output function from a given 2-valued input 2-valued output functions. Then, it constructs a 4-valued decision diagram (4-valued DD) to represent the generated 4-valued input function. Finally, it selects a good expansion among 27 different expansions for each 4-valued node of the 4-valued DD and derive a 4-valued PKDD. We present heuristics to produce compact 4-valued PKDDs. Experimental results using benchmark functions show the efficiency of our method. From experiments, we also conjecture that, for n>1, to represent an n-bit adder (adr n), a 4-valued PKDD, a 4-valued DD (MDD), a 2-valued PKDD, and a shared binary decision diagram (SBDD) require 2n+1, 3n-1, 4n-1, and 9n-7 non-terminal nodes, respectively.