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Dystopian // Berlin Underground // Electronic // Minimal Synth // Wave // Melancholy, inteligent dark side 유 Tech.body
VESNACH

[https://i.nyx.cz/files/00/00/21/27/2127529_d458341feaf49afcd0c8.jpg?name=LHI6EQ6HE74OCTVSC4Q7BRVLTY.jpeg]
We prove a separation between monotone and general arithmetic formulas for polynomials of constant degree. We give an example of a polynomial C in n variables and degree k which is computable by a homogeneous arithmetic formula of size O(k 2n 2 ), but every monotone formula computing C requires size (n/kc ) Ω(log k) , with c ∈ (0, 1). Since the upper bound is achieved by a homogeneous arithmetic formula, we also obtain a separation between monotone and homogeneous formulas, for polynomials of lipsum constant degree
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VESNACH --- 2:13:01 26.5.2020
VESNACH --- 21:39:22 25.5.2020
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VESNACH --- 17:20:09 23.5.2020