Root finding with threshold circuits

Details Root finding with threshold circuits Root finding with threshold circuits

2011-12-16

arxiv.org/abs/1112.3925v1

Computer Science

Data Structures and Algorithms

19 pages, 1 figure

Scientific paper

We show that for any constant d, complex roots of degree d univariate rational (or Gaussian rational) polynomials---given by a list of coefficients in binary---can be computed to a given accuracy by a uniform TC^0 algorithm (a uniform family of constant-depth polynomial-size threshold circuits). The basic idea is to compute the inverse function of the polynomial by a power series. We also discuss an application to the theory VTC^0 of bounded arithmetic.

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