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

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...

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Bibliographic Details
Published inIEEE transactions on computers Vol. C-34; no. 2; pp. 131 - 140
Main Author SASAO, T
Format Journal Article
LanguageEnglish
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
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ISSN0018-9340
1557-9956
DOI10.1109/TC.1985.1676549

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Summary: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.
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.1985.1676549