Root finding with threshold circuits

Emil Jeřábek

doi:10.1016/j.tcs.2012.09.001

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arXiv · 1112.3925

Root finding with threshold circuits

Emil Jeřábek

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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 VTC^0 of bounded arithmetic.

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Emil Jeřábek. 2012-10-23. Root finding with threshold circuits. https://doi.org/10.1016/j.tcs.2012.09.001

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