Geodesic
Generalization of complexity estimates for flat circuits realizing partial Boolean operators
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 60-64

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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. 
@article{VMUMM_2018_3_a9,
     author = {G. V. Kalachev},
     title = {Generalization of complexity estimates for flat circuits realizing partial {Boolean} operators},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {60--64},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a9/}
}
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G. V. Kalachev. Generalization of complexity estimates for flat circuits realizing partial Boolean operators. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 60-64. http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a9/