Improved Bounds for Reduction to Depth 4 and Depth 3
نویسنده
چکیده
Koiran [8] showed that if an n-variate polynomial fn of degree d (with d = n) is computed by a circuit of size s, then it is also computed by a homogeneous circuit of depth four and of size 2 √ d log(n) . Using this result, Gupta, Kamath, Kayal and Saptharishi [7] found an upper bound for the size of a depth three circuit computing fn. We improve here Koiran’s bound. Indeed, we show that it is possible to transform an arithmetic circuit into a depth four circuit of size 2 (
منابع مشابه
Superpolynomial Lower Bounds for General Homogeneous Depth 4 Arithmetic Circuits
In this paper, we prove superpolynomial lower bounds for the class of homogeneous depth 4 arithmetic circuits. We give an explicit polynomial in VNP of degree n in n variables such that any homogeneous depth 4 arithmetic circuit computing it must have size n . Our results extend the works of Nisan-Wigderson [NW95] (which showed superpolynomial lower bounds for homogeneous depth 3 circuits), Gup...
متن کاملA From Sylvester-Gallai Configurations to Rank Bounds: Improved Blackbox Identity Test for Depth-3 Circuits
We study the problem of identity testing for depth-3 circuits of top fanin k and degree d. We give a new structure theorem for such identities that improves the known deterministic d O(k) -time blackbox identity test over rationals (Kayal & Saraf, FOCS 2009) to one that takes dO(k 2)-time. Our structure theorem essentially says that the number of independent variables in a real depth-3 identity...
متن کاملMonitoring sugar beet rooting depth irrigated with recycled waste water and different irrigation methods for water savings in an arid climate
ABSTRACT- A detailed understanding of crop rooting systems will facilitate water use reduction, optimized nutrient uptake and irrigation scheduling more efficiently. A field experiment was conducted during 2005-2006 to investigate sugar beet rooting depth growth, irrigated with three irrigation methods (subsurface drip, surface drip and furrow) and two water qualities (recycled wastewater: EC= ...
متن کاملتأثیر بار محوری و بار کششی بر بازده زمین گیرایی و مصرف سوخت دو تراکتور سنگین در اجرای شخم با گاوآهن برگردان دار چهار خیش نیمه سوار
Tractive efficiency and fuel consumption of Massey Ferguson (MF399) and John Deere (JD 4230) tractors during plowing with moldboard plow were evaluated and compared. The tests were conducted at the Experimental Station, College of Agriculture, Shiraz University, in a field with sandy clay soil at average moisture content of 18% d. b. from zero to 30 cm depth. A randomized complete block d...
متن کاملAn Approach for Operation Depth Reduction of an Underwater Glider Propelled by Ocean Thermal Energy
The underwater Gliders are a kind of autonomous vehicles that have a special role in ocean surveys which demand continuous monitoring and long endurance. Because of low energy consumption and long endurance, these vehicles are favorite for these missions. Among this, a type of gliders can harvest ocean thermal energy, causing significant endurance increase. These vehicles need at least 680 mete...
متن کامل