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On the Arithmetic Complexity of Euler Function

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Computer Science – Theory and Applications (CSR 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6651))

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Abstract

It is shown that the problem of computing the Euler function is closely related to the problem of computing the permanent of a matrix as well as to the derandomization of the Identity Testing problem. Specifically, it is shown that (1) if computing the Euler function over a finite field is hard then computing permanent over the integers is also hard, and (2) if computing any factor of the Euler function over a field is hard then the Identity Testing problem over the field can be derandomized.

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Author information

Authors and Affiliations

  1. IIT Kanpur, India

    Manindra Agrawal

Authors
  1. Manindra Agrawal
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Editors and Affiliations

  1. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, 191023, St.Petersburg, Russia

    Alexander Kulikov

  2. Department of Mathematical Logic and Theory of Algorithms, Moscow State University, Leninskie gory, 119991, Moscow, Russia

    Nikolay Vereshchagin

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Agrawal, M. (2011). On the Arithmetic Complexity of Euler Function. In: Kulikov, A., Vereshchagin, N. (eds) Computer Science – Theory and Applications. CSR 2011. Lecture Notes in Computer Science, vol 6651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20712-9_4

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  • DOI: https://doi.org/10.1007/978-3-642-20712-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20711-2

  • Online ISBN: 978-3-642-20712-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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