Worst and Best Irredundant Sum-of-Products Expressions
Abstract
ÐIn an irredundant sum-of-products expression (ISOP), each product is a prime implicant (PI) and no product can be deleted
without changing the function. Among the ISOPs for some function f, a worst ISOP (WSOP) is an ISOP with the largest number of PIs
and a minimum ISOP (MSOP) is one with the smallest number. We show a class of functions for which the Minato-Morreale ISOP
algorithm produces WSOPs. Since the ratio of the size of the WSOP to the size of the MSOP is arbitrarily large when n, the number of
variables, is unbounded, the Minato-Morreale algorithm can produce results that are very far from minimum. We present a class of
multiple-output functions whose WSOP size is also much larger than its MSOP size. For a set of benchmark functions, we show the
distribution of ISOPs to the number of PIs. Among this set are functions where the MSOPs have almost as many PIs as do the
WSOPs. These functions are known to be easy to minimize. Also, there are benchmark functions where the fraction of ISOPs that are
MSOPs is small and MSOPs have many fewer PIs than the WSOPs. Such functions are known to be hard to minimize. For one class of
functions, we show that the fraction of ISOPs that are MSOPs approaches 0 as n approaches infinity, suggesting that such functions
are hard to minimize.
Description
IEEE Transactions on Computers, Vol. 50, No. 9, September 2001
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.
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