Geodesic
On the recognition problem for algebraic threshold functions
Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 206-211

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We prove the existence of recognition algorithm for algebraic Boolean threshold functions by calculating upper bounds of absolute values of modulo and coefficients of a linear form. The modulo bound looks like $(n+3)^{(n+5)/2}/2^{n+2}$ and the bound of algorithm complexity is O$(({{n}/{2}})^{n^2})$.
Keywords: recognition problem, algebraic threshold functions. 
@article{PDMA_2019_12_a57,
     author = {S. V. Jenevsky and S. L. Melnikov and A. N. Shurupov},
     title = {On the recognition problem for algebraic threshold functions},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {206--211},
     publisher = {mathdoc},
     number = {12},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2019_12_a57/}
}
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S. V. Jenevsky; S. L. Melnikov; A. N. Shurupov. On the recognition problem for algebraic threshold functions. Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 206-211. http://geodesic.mathdoc.fr/item/PDMA_2019_12_a57/