1 research outputs found
Compact DSOP and partial DSOP Forms
Given a Boolean function f on n variables, a Disjoint Sum-of-Products (DSOP)
of f is a set of products (ANDs) of subsets of literals whose sum (OR) equals
f, such that no two products cover the same minterm of f. DSOP forms are a
special instance of partial DSOPs, i.e. the general case where a subset of
minterms must be covered exactly once and the other minterms (typically
corresponding to don't care conditions of ) can be covered any number of
times. We discuss finding DSOPs and partial DSOP with a minimal number of
products, a problem theoretically connected with various properties of Boolean
functions and practically relevant in the synthesis of digital circuits.
Finding an absolute minimum is hard, in fact we prove that the problem of
absolute minimization of partial DSOPs is NP-hard. Therefore it is crucial to
devise a polynomial time heuristic that compares favorably with the known
minimization tools. To this end we develop a further piece of theory starting
from the definition of the weight of a product p as a functions of the number
of fragments induced on other cubes by the selection of p, and show how product
weights can be exploited for building a class of minimization heuristics for
DSOP and partial DSOP synthesis. A set of experiments conducted on major
benchmark functions show that our method, with a family of variants, always
generates better results than the ones of previous heuristics, including the
method based on a BDD representation of f