On Some Complexity Issues of NC Analytic Functions

  • Fuxiang Yu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)


This paper studies the complexity of derivatives and integration of NC real functions (not necessarily analytic) and NC analytic functions. We show that for NC real functions, derivatives and integration are infeasible, but analyticity helps to reduce the complexity. For example, the integration of a log-space computable real function f is as hard as #P, but if f is an analytic function, then the integration is log-space computable. As an application, we study the problem of finding all zeros of an NC analytic function inside a Jordan curve and show that, under a uniformity condition on the function values of the Jordan curve, the zeros are all NC computable.


Meromorphic Function Turing Machine Complexity Class Jordan Curve Modulus Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Fuxiang Yu
    • 1
  1. 1.Department of Computer ScienceState University of New York at Stony BrookStony BrookUSA

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