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Computing Elementary Symmetric Polynomials with a Sub-Polynomial .. - Grolmusz (2002) (Correct)
....jIj=k Y x i (1) modulo non prime power composite numbers with a much smaller number of multiplications than it is possible over rationals or prime moduli. Our model of computation is the arithmetic circuit model of depth 3, circuits in this model are often called Sigma Pi Sigma circuits [17] [22]. Sigma Pi Sigma circuits perform computations of the following form: s i j=1 (a ij1 x 1 a ij2 x 2 Delta Delta Delta a ijn x n b ij ) If all the b ij = 0 and all the s i s are the same number, then the circuit is called a homogeneous circuit, otherwise it is inhomogeneous. The ....
....necessary. The optimum upper bound for the odd cover was proved by Radhakrishnan, Sen and Vishwanathan [17] Radhakrishnan, Sen and Vishwanathan also gavematching upper bounds for covers, when the off diagonal elements of matrix M are covered bymultiplicity 1 modulo a prime. By a result of Ben Or [22], every elementary symmetric polynomial S n (and similarly, every symmetric function) can be computed over fields by size O(n ) inhomogeneous Sigma Pi Sigma circuits, using one variable polynomial interpolation. This result shows the power of arithmetic circuits over Boolean circuits with MOD ....
A. Shpilka. PhD. Thesis, Hebrew University 2001. http://www.cs.huji.ac.il/amirs/publications/my main.ps.gz.
Computing Elementary Symmetric Polynomials with a Sub-Polynomial .. - Grolmusz (2002) (Correct)
No context found.
A. Shpilka. PhD. Thesis, Hebrew University 2001. http://www.cs.huji.ac.il/amirs/publications/my main.ps.gz.
Computing Elementary Symmetric Polynomials with a Sub-Polynomial .. - Grolmusz (2002) (Correct)
No context found.
A. Shpilka. PhD. Thesis, Hebrew University 2001. http://www.cs.huji.ac.il/amirs/publications/my main.ps.gz.
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