F. Green, A complex-number fourier method for lower bounds on the Mod-m degree, in Computational Complexity, 9 (2000) 16 - 38.  Home/Search   Document Not in Database   Summary   Related Articles

....weaker circuit models [BT] GKRST] that still are at least as powerful as quasipolynomial size MAJ MOD 2 AND (log n) O(1) However, the relationship between MAJ MOD 2 AND (log n) O(1) circuits and ACC remains unresolved. This is the central motivating problem we address. See [Gr99] and [Gr00] for somewhat di erent perspectives. This problem shares some of the diculties of nding lower bounds for depth 2 and depth 3 threshold circuits. Among the strongest lower bounds of this type is the result of H astad and Goldmann [HG] that says that the generalized inner product function ....

....equation (12) is a partial sum, i.e. the variables y i do not range over the entire eld Z 5 . It is possible to re formulate the discriminator so as to obtain character sums that range over the complete eld, by encoding eld elements in the Boolean variables along the lines of [BS] KP] and [Gr00] However, the degrees of the polynomials are then higher than 2, and we are back to the problem of higher degree polynomials. Despite these problems, we believe at this point that they are not particularly dicult and that an appropriate algebraic setting will resolve them. Acknowledgements: ....

F. Green, A complex-number fourier method for lower bounds on the Mod-m degree, in Computational Complexity, 9 (2000) 16 - 38.

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