Geodesic
Minimization of representations of the logical function in Schaeffer and Pierce bases
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 14 (2022) no. 4, pp. 20-27

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The paper studies the representation of arbitrary logical functions in Schaeffer and Pierce bases. For this purpose, recurrent dependencies of the representation of disjunctive and conjunctive monomials in these bases were initially established. Then generalizations were made to the arbitrary logical formulas presented in the form of disjunctive and conjunctive normal forms. Estimates were obtained for the number of operations in logical formulas during the transition to the Schaeffer and Pierce bases.
Keywords: disjunctive monomial, conjunctive monomial, Schaeffer's basis, Pierce's basis, Boolean variable, Boolean function. 
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     author = {V. V. Menshikh and V. A. Nikitenko},
     title = {Minimization of representations of the logical function in {Schaeffer} and {Pierce} bases},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
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     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2022_14_4_a2/}
}
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V. V. Menshikh; V. A. Nikitenko. Minimization of representations of the logical function in Schaeffer and Pierce bases. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 14 (2022) no. 4, pp. 20-27. http://geodesic.mathdoc.fr/item/VYURM_2022_14_4_a2/