On the asymptotics of the number of repetition-free Boolean functions in the basis $\{\,\lor,\oplus,\lnot\}$
Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 158-159
We obtain an asymptotic formula for the number $S_n$ of repetition-free Boolean functions of $n$ variables in the basis $\{\,\lor,\oplus,\lnot\}$ for $n\to\infty: S_n\sim cn^{-3/2}\alpha^nn!$, where $c\approx0.1998398363\;,\alpha\approx7.549773429\;.$
Keywords:
repetition-free Boolean function, enumeration, asymptotics.
@article{DM_2015_27_3_a10,
author = {V. A. Voblyi},
title = {On the asymptotics of the number of repetition-free {Boolean} functions in the basis $\{\&,\lor,\oplus,\lnot\}$},
journal = {Diskretnaya Matematika},
pages = {158--159},
year = {2015},
volume = {27},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_2015_27_3_a10/}
}
TY - JOUR
AU - V. A. Voblyi
TI - On the asymptotics of the number of repetition-free Boolean functions in the basis $\{\&,\lor,\oplus,\lnot\}$
JO - Diskretnaya Matematika
PY - 2015
SP - 158
EP - 159
VL - 27
IS - 3
UR - http://geodesic.mathdoc.fr/item/DM_2015_27_3_a10/
LA - ru
ID - DM_2015_27_3_a10
ER -
V. A. Voblyi. On the asymptotics of the number of repetition-free Boolean functions in the basis $\{\&,\lor,\oplus,\lnot\}$. Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 158-159. http://geodesic.mathdoc.fr/item/DM_2015_27_3_a10/
[1] Izbrannye voprosy teorii bulevykh funktsii, Pod red. S.F. Vinokurova i N.A. Peryazeva, Fizmatlit, Moskva, 2001, 192 pp.
[2] Zubkov O.V., “Uluchshennye otsenki chisla bespovtornykh bulevykh funktsii v polnom binarnom bazise $\{\,\lor,\oplus,\lnot\}$”, Matem. zametki, 87:5 (2010), 721–733 | DOI | MR | Zbl
[3] Voblyi V.A., “Asimptotika chisla bespovtornykh bulevykh funktsii v bazise $B_1$”, Diskretnaya matematika, 22:4 (2010), 156–157 | DOI | MR | Zbl
[4] Lavrentev M.A., Shabat B.M., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1965, 716 pp. | MR