This paper first reviews the trends of VLSI design, focusing on the power dissipation and programmability. Then, we show the advantage of Quarternary Decision Diagrams (QDDs) in representing and evaluating logic functions. That is, we show how QDDs are used to implement QDD machines, which yield high-speed implementations. We compare QDD machines with binary decision diagram (BDD) machines, and...

This paper addresses the problem of binary decision diagram (BDD) minimization in the presence of don’t caresets. Specifically, given an incompletely specified function g and a fixed ordering of the variables, we propose anexact algorithm for selectingf such that f is a cover for g and the binary decision diagram for f is of minimumsize. The approach described is the only kn...

This paper addresses the problem of binary decision diagram (BDD) minimization in the presence of don’t care sets. Specifically, given an incompletely specified function g and a fixed ordering of the variables, we propose an exact algorithm for selecting f such that f is a cover for g and the binary decision diagram for f is of minimum size. The approach described is the only known exact algori...

This paper addresses the problem of binary decision diagram (BDD) minimization in the presence of don’t care sets. Specifically, given an incompletely specified function and a fixed ordering of the variables, we propose an exact algorithm for selecting such that is a cover for and the binary decision diagram for is of minimum size. The approach described is the only known exact algorithm for th...

We address the problem of permutation independent comparison of two pseudo Boolean functions given by multiplicative binary moment diagrams (∗Bmds), i. e., the problem of deciding whether there exists a permutation of the input variables such that the two ∗Bmds are equal. The analogous problem has already been investigated for binary decision diagrams (Bdds) in detail [5, 7, 8, 9, 10]. All thes...

It is well-known that the size of an ordered binary decision diagram (OBDD) may depend crucially on the order in which the variables occur. In the paper, we describe an implementation of an output{ eecient algorithm that transforms an OBDD P representing a Boolean function f with respect to one variable ordering into an OBDD Q that represents f with respect to another variable ordering. The alg...

Many advances in argumentation theory have been made, but the exponential complexity of argumentation-based reasoning has made it impractical to apply argumentation theory. In this paper, we propose a binary decision diagram (BDD) approach to argumentation-based reasoning. In the approach, sets of arguments and defeats are encoded into BDDs so that an argumentation process can work on a set of ...

This paper proposes a high-speed architecture to realize two-variable numeric functions. It represents the given function as an edgevalued multiple-valued decision diagram (EVMDD), and shows a systematic design method based on the EVMDD. To achieve a design, we characterize a numeric function f by the values of l and p for which f is an l-restricted Mp-monotone increasing function. Here, l is a...

We consider the problem of testing whether a function f : {0, 1} → {0, 1} is computable by a read-once, width-2 ordered binary decision diagram (OBDD), also known as a branching program. This problem has two variants: one where the variables must occur in a fixed, known order, and one where the variables are allowed to occur in an arbitrary order. We show that for both variants, any nonadaptive...