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2002
Springer

On the hardness of approximating the permanent of structured matrices

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On the hardness of approximating the permanent of structured matrices
We show that for several natural classes of "structured" matrices, including symmetric, circulant, Hankel and Toeplitz matrices, approximating the permanent modulo a prime p is as hard as computing its exact value. Results of this kind are well known for arbitrary matrices. However the techniques used do not seem to apply to "structured" matrices. Our approach is based on recent advances in the hidden number problem introduced by Boneh and Venkatesan in 1996 combined with some bounds of exponential sums motivated by the Waring problem in finite fields. Keywords. Approximation of the permanent, hidden number problem, exponential sums. Subject classification. 11T23, 15A15, 68Q17.
Bruno Codenotti, Igor Shparlinski, Arne Winterhof
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2002
Where CC
Authors Bruno Codenotti, Igor Shparlinski, Arne Winterhof
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