New multivalued functional decomposition algorithms based on MDDs

Abstract

Abstract-This paper presents two new functional decomposition partitioning algorithms that use multivalued decision diagrams (MDDs). MDDs are an exceptionally good representation for generalized decomposition because they are canonical and they can represent very large functions. Algorithms developed in this paper are for Boolean/multivalued input and output, completely/incompletely specified functions with application to logic synthesis, machine learning, data mining and knowledge discovery in databases. We compare the run-times and decision diagram sizes of our algorithms to existing decomposition partitioning algorithms based on decision diagrams. The comparisons show that our algorithms are faster and do not result in exponential diagram sizes when decomposing functions with small bound sets.Index Terms-Algorithms, logic design, unsupervised learning.

An input variable partitioning algorithm for functional decomposition of a system of Boolean functions based on the tabular method

“…The subsets Z 1 and Z 2 are called bound and free sets, respectively. A few papers deal with the search for the partition {Z 1 , Z 2 } at which this problem has a solution [2,9,18,29,21,16,7,19]. In this paper, the main attention is paid to the search for subsets Z 1 and Z 2 in a particular way.…”

A Generalized If-Then-Else Operator for the Representation of Multi-Output Functions

“…The system of logic functions can be considered as a single function of input Boolean variables and Boolean output variables. Such functions are called multi-output functions (MOFs) [10,11,[20][21][22][23]. The domain and range of an MOF are thedimensional and -dimensional Boolean cubes, B and B , respectively.…”

“…One such topic is "systems of logic functions" (logic systems) and their corresponding representations. The most popular representations of logic systems are (a) the matrix (which is actually a Karnaugh-like form) and (b) the Multiterminal Binary Decision Diagram (MTBDD) [10][11][12][13][14]. There are three known ways to treat and optimize systems of logic functions: (a) as a set of single decision diagrams with two terminal nodes that may share conditional nodes (Shared Binary Decision Diagrams (SBDDs)) [15]; (b) as a single, so-called characteristic function, where the output of each function of the system is considered to be an additional input variable of the characteristic function [16]; (c) as a single decision diagram whose terminals are words [14].…”

Variability-Aware Design of Multilevel Logic Decoders for Nanoscale Crossbar Memories

“…The simplification and minimization of EXOR-sum-of-product expressions for MVL functions were presented in [25] and [29], respectively. The use of MV functional decomposition algorithms based on MV decision diagrams was investigated in [10] for logic synthesis. The efficient minimization of MVL networks with don't-cares was presented in [14] as a way to implement MVL hardware and also as an optimization opportunity for binary functions at the MV stage, which cannot be discovered in the binary domain.…”

“…While interconnects cannot follow the scaling of transistors, MV wires can carry denser information and reduce the area dedicated to global interconnects [27], [28]. MVL can be also implemented in hardware for computation [7], [21], and many MVL minimizers and input/output encoders exist [10], [23], [25] and have proved their superior performance.…”