Geodesic
Thin circulant matrixes and lower bounds on complexity of some Boolean operators
Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 5, pp. 38-53

Voir la notice de l'article provenant de la source Math-Net.Ru

Lower estimate $\Omega(\frac{k+l}{k^2l^2}N^{2-\frac{k+l+2}{kl}})$ of the maximal possible weight of a $(k,l)$-thin (that is, free of all-ones' submatrixes of size $k\times l$) circulant matrix of order $N$ is proved. The estimate is close to the known estimate corresponding to the class of all $(k,l)$-thin matrixes. As a consequence, new estimates of several complexity measures of Boolean sums' systems and a lower estimate $\Omega(N^2\log^{-6}N)$ of monotone complexity of a Boolean convolution of order $N$ are obtained. Ill. 1, bibliogr. 11.
Keywords: complexity, thin matrix, Zarankiewicz problem, Boolean sum
Mots-clés : circulant matrix, monotone circuit, rectifier circuit, Boolean convolution. 
@article{DA_2011_18_5_a2,
     author = {M. I. Grinchuk and I. S. Sergeev},
     title = {Thin circulant matrixes and lower bounds on complexity of some {Boolean} operators},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {38--53},
     publisher = {mathdoc},
     volume = {18},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2011_18_5_a2/}
}
TY  - JOUR
AU  - M. I. Grinchuk
AU  - I. S. Sergeev
TI  - Thin circulant matrixes and lower bounds on complexity of some Boolean operators
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2011
SP  - 38
EP  - 53
VL  - 18
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2011_18_5_a2/
LA  - ru
ID  - DA_2011_18_5_a2
ER  - 
%0 Journal Article
%A M. I. Grinchuk
%A I. S. Sergeev
%T Thin circulant matrixes and lower bounds on complexity of some Boolean operators
%J Diskretnyj analiz i issledovanie operacij
%D 2011
%P 38-53
%V 18
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2011_18_5_a2/
%G ru
%F DA_2011_18_5_a2
M. I. Grinchuk; I. S. Sergeev. Thin circulant matrixes and lower bounds on complexity of some Boolean operators. Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 5, pp. 38-53. http://geodesic.mathdoc.fr/item/DA_2011_18_5_a2/