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On Some Complexity Issues of NC Analytic Functions

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Theory and Applications of Models of Computation (TAMC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3959))

Abstract

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.

This material is based upon work supported by National Science Foundation under grant No. 0430124.

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Author information

Authors and Affiliations

  1. Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY, 11794, USA

    Fuxiang Yu

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  1. Fuxiang Yu
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Editor information

Editors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, 53706, Madison, WI, USA

    Jin-Yi Cai

  2. School of Mathematics, University of Leeds, LS2 9JT, Leeds, U.K.

    S. Barry Cooper

  3. State Key Lab. of Computer Science, Institute of Software, Chinese Academy of Sciences,  

    Angsheng Li

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© 2006 Springer-Verlag Berlin Heidelberg

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Yu, F. (2006). On Some Complexity Issues of NC Analytic Functions. In: Cai, JY., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2006. Lecture Notes in Computer Science, vol 3959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11750321_36

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  • DOI: https://doi.org/10.1007/11750321_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34021-8

  • Online ISBN: 978-3-540-34022-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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