Geodesic
Some structural properties of quadratic Boolean threshold functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 48-51.

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With the help of a binary partial order relation on the set of quadratic forms with Boolean variables, some classes of simultaneously decomposed (or not having any decompositions) quadratic Boolean threshold functions are described. Simple representatives of these classes are pointed out. In some cases, we can prove whether a variable is essential or not for a quadratic Boolean threshold functions.
Keywords: quadratic Boolean threshold function, essential variable.
Mots-clés : decomposition 
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A. N. Shurupov. Some structural properties of quadratic Boolean threshold functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 48-51. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a17/

[1] Podolskii V. V., Otsenki vesov perseptronov (polinomialnykh porogovykh bulevykh funktsii), Avtoref. dis. $\dots$ kand. fiz.-mat. nauk, MGU im. M. V. Lomonosova, M., 2009

[2] Shurupov A. N., “O funktsionalnoi razdelimosti bulevykh porogovykh funktsii”, Diskretnaya matematika, 9:2 (1997), 59–73 | DOI | MR | Zbl

[3] Khachiyan L. G., “Polinomialnyi algoritm v lineinom programmirovanii”, Dokl. AN SSSR, 244:5 (1979), 1033–1096 | MR

[4] Dreo J., Petrowski A., Siarry P., Taillard E., Metaheuristics for Hard Optimisation. Methods and Case Studies, Springer, 2006, 372 pp. | MR

[5] Khokhlyuk V. I., Pryamoi metod tselochislennoi optimizatsii, In-t matematiki im. S. L. Soboleva, Novosibirsk, 2002, 38 pp.

[6] Crama Y., Hammer P., Boolean Functions. Theory, Algorithms and Applications, Cambridge University Press, 2011 | MR | Zbl