Geodesic
Asymptotics for the Complexity of Boolean Functions with Small Number of Ones
Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 257-263

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The class $F_{n,k}$ of Boolean functions consisting of all functions of $n$ variables each of which outputs $1$ at exactly $k$ $n$-tuples of values of the variables is considered. For small $k$, for example, for $k\ln n$, an asymptotics for the complexity of implementation of every function in $F_{n,k}$ by a circuit of functional elements in an irredundant basis containing $x\to y$ and $\overline{x\to y}$ is found.
Keywords: Boolean function, complexity of a function.
Mots-clés : circuit 
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     author = {N. P. Red'kin},
     title = {Asymptotics for the {Complexity} of {Boolean} {Functions} with {Small} {Number} of {Ones}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {257--263},
     publisher = {mathdoc},
     volume = {109},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_2_a8/}
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N. P. Red'kin. Asymptotics for the Complexity of Boolean Functions with Small Number of Ones. Matematičeskie zametki, Tome 109 (2021) no. 2, pp. 257-263. http://geodesic.mathdoc.fr/item/MZM_2021_109_2_a8/