Root finding with threshold circuits

Authors:
Emil Jeábek
Affiliations:
-
Venue:
Theoretical Computer Science
Year:
2012

Citing 17
Cited 1

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Abstract

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 V TC^0 of bounded arithmetic.