This paper proposes a method to construct smaller binary decision diagrams for characteristic functions (BDDs for CFs). A BDD for CF represents an n-input m-output function, and evaluates all the outputs in O(n+m) time. We derive an upper bound on the number of nodes of the BDD for CF of n-bit adders (adrn). We also compare complexities of BDDs for CFs with those of shared binary decision diagrams (SBDDs) and multi-terminal binary decision diagrams (MTBDDs). Our experimental results show: 1) BDDs for CFs are usually much smaller than MTBDDs; 2) for adrn and for some benchmark circuits, BDDs for CFs are the smallest among the three types of BDDs; and 3) the proposed method often produces smaller BDDs for CFs than an existing method.

In this paper, we propose a compact representation of logic functions using Multi-valued Decision Diagrams (MDDs) called heterogeneous MDDs. In a heterogeneous MDD, each variable may take a different domain. By partitioning binary input variables and representing each partition as a single multi-valued variable, we can produce a heterogeneous MDD with 16% smaller memory size than a Reduced Ordered Binary Decision Diagram (ROBDD), and with comparable memory size to Free Binary Decision Diagrams (FBDDs). And also, heterogeneous MDDs have shorter Average Path Length (APL) than ROBDDs and FBDDs. We minimized a large number of benchmark functions to show the compactness of heterogeneous MDDs.