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JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018 Number 3, Pages 60–64 (Mi vmumm35)

This article is cited in 2 papers

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Generalization of complexity estimates for flat circuits realizing partial Boolean operators

G. V. Kalachev

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper we consider the Shannon function of plain circuit activity for class of partial Boolean operators with restrictions on the number of different operator values. It is proved that for the class of partial operators with $m$ outputs, domain of cardinality $d$, and the number of different values not exceeding $r$ the mean and maximal orders of activity are equal to $(\sqrt{d}+m\sqrt{r}/\log r)\sqrt{\log r}$ by the order.

Key words: plain circuits, activity, potential, Shannon function, lower bounds, upper bounds, Boolean operators.

UDC: 519.714

Received: 27.09.2017


 English version:
Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 2018, 73:3, 120–123

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