Issue No.05 - May (1996 vol.45)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/12.509916
<p><b>Abstract</b>—Boolean function complementation is a basic operation of Boolean algebra. For functions given in SOP form, the complementation methods include the DeMorgan's Law, sharp [<ref rid="bibt06263" type="bib">3</ref>], disjoint sharp[<ref rid="bibt06262" type="bib">2</ref>], unate complementation [<ref rid="bibt06264" type="bib">4</ref>], recursive [<ref rid="bibt06264" type="bib">4</ref>], and Sasao's method [<ref rid="bibt06265" type="bib">5</ref>].</p><p>This paper accomplishes three purposes: 1) It exposes an underlying unification of the existing complementation algorithms. It is proven that a) unate-complementation and sharp are the same as the DeMorgan Law algorithm; b) Sasao's algorithm is the same as disjoint sharp; c) disjoint sharp is a special case of the recursive method. 2) It proposes negation trees for the representation of functions and their complements, and 3) it gives faster algorithms for finding complements of functions in SOP form based on negation trees.</p>
Boolean functions, unate functions, complementation algorithms, negation trees.
Yuke Wang, Carl McCrosky, "Negation Trees: A Unified Approach to Boolean Function Complementation", IEEE Transactions on Computers, vol.45, no. 5, pp. 626-630, May 1996, doi:10.1109/12.509916