Abstract
It was previously established that almost every Boolean function of n variables with k zeros, where k is at most log2 n–log2log2 n + 1, can be associated with a Boolean function of 2k–1–1 variables with k zeros (complete function) such that the complexity of implementing the original function in the class of disjunctive normal forms is determined only by the complexity of implementing the complete function. An asymptotically tight bound is obtained for the minimum possible number of literals contained in the disjunctive normal forms of the complete function.
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Original Russian Text © Yu.V. Maximov, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 7, pp. 1266–1280.
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Maximov, Y.V. Shortest and minimal disjunctive normal forms of complete functions. Comput. Math. and Math. Phys. 55, 1242–1255 (2015). https://doi.org/10.1134/S0965542515070106
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DOI: https://doi.org/10.1134/S0965542515070106