An Algorithm to Derive the Complement of a Binary Function with Multiple-Valued Inputs

• Published in: IEEE transactions on computers Vol. C-34; no. 2; pp. 131 - 140
• Main Author: SASAO, T
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.1985; Institute of Electrical and Electronics Engineers
• Subjects: Absorption; Applied sciences; Complement of logical expression; Computer science; control theory; systems; Computers; Decoding; Exact sciences and technology; Logic; logic design; Logical, boolean and switching functions; Memory management; Minimization; minimization of logical expressions; multiple valued logic; prime implicants; programmable logic array; Programmable logic arrays; Silicon; Switches; switching theory; Theoretical computing; Logical function; Minimization; Algorithm; Recursivity; Programmable logic array
• ISSN: 0018-9340; 1557-9956
• DOI: 10.1109/TC.1985.1676549

A recursive algorithm to obtain a complement of a sum-of-products expression for a binary function with p-valued inputs is presented. It produces at most pn/2 products for n-variable functions, whereas a conventional elementary algorithm produces O(tn·n(1-t)/2) products where t = 2P -1. It is 10-20 times faster than the elementary one when p = 2 and n = 8. For large practical-problems, it produces many fewer products than the disjoint sharp algorithm used by MINI. Appplications of the algorithm to PLA minimization are also presented.