Geodesic
Representations of normalized formulas
Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 4, pp. 77-103

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A class of objects called $\Pi$-partitions is defined. These objects, in a certain well-defined sense, are the equivalents of formulas in a basis consisting of disjunction, conjunction and negation, in which negations are possible only over variables (normalized formulas). $\Pi$-partitions are seen as representations of formulas, just as equivalents and graphical representations of the same formulas can be considered $\Pi$-schemes. Some theory of such representations has been developed which is essentially a mathematical apparatus focused on describing a class of minimal normalized formulas implementing linear Boolean functions. Bibliogr. 18.
Keywords: Boolean function, normalized formula, representation of a formula, $\Pi$-scheme, lower bound for the complexity.
Mots-clés : minimal formula, $\Pi$-partition 
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K. L. Rychkov. Representations of normalized formulas. Diskretnyj analiz i issledovanie operacij, Tome 29 (2022) no. 4, pp. 77-103. http://geodesic.mathdoc.fr/item/DA_2022_29_4_a4/