On parallel complexity of analytic functions.

Abstract: In this paper, we study the parallel complexity of analytic functions. We investigate the complexity of computing the derivatives, integrals, and zeros of or logarithmic-space computable analytic functions, where denotes the complexity class of sets acceptable by polynomial-size, polylogarithmic-depth, uniform Boolean circuits. It is shown that the derivatives and integrals of (or logarithmic-space) computable analytic functions remain (or, respectively, logarithmic-space) computable. We also study the problem of finding all zeros of an computable analytic function inside an computable Jordan curve, and show that, under a uniformity condition on the function values on the Jordan curve, all zeros can be found in . [Copyright &y& Elsevier]