Irredundant Normal Forms and Minimal Dependence Sets of a Boolean Function

A new method is presented for determining all minimal dependence sets, irredundant normal forms, and irredundant normal forms of minimal dependence sets of a Boolean function f. The method reduces the above problems into those of determining all minimal positive dependence sets, irredundant positive...

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Bibliographic Details
Published inIEEE transactions on computers Vol. C-27; no. 11; pp. 1064 - 1068
Main Authors Halatsis, Gaitanis
Format Journal Article
LanguageEnglish
Published IEEE 01.11.1978
Subjects
Boolean functions
dependence sets
irredundant normal forms
minimization
positive functions
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Summary:A new method is presented for determining all minimal dependence sets, irredundant normal forms, and irredundant normal forms of minimal dependence sets of a Boolean function f. The method reduces the above problems into those of determining all minimal positive dependence sets, irredundant positive normal forms, and irredundant positive normal forms of minimal positive dependence sets, respectively, of a Boolean function f* corresponding to f. For each problem a corresponding cover formula is developed such that the prime implicants of it are in one-to-one correspondence to all possible solutions.
ISSN:0018-9340
1557-9956
DOI:10.1109/TC.1978.1674997