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International Colloquium on Automata, Languages, and Programming

ICALP 2015: Automata, Languages, and Programming pp 810–821Cite as

Lower Bounds for Sums of Powers of Low Degree Univariates

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9134))

Abstract

We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degree polynomials. We prove a lower bound of \(\Omega \left( \sqrt{\frac{d}{t}} \right) \) for writing an explicit univariate degree-d polynomial f(x) as a sum of powers of degree-t polynomials.

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Author information

Authors and Affiliations

  1. Microsoft Research India, Bengaluru, India

    Neeraj Kayal

  2. Ecole Normale Supérieure de Lyon, Lyon, France

    Pascal Koiran & Timothée Pecatte

  3. Indian Institute of Science, Bengaluru, India

    Chandan Saha

Authors
  1. Neeraj Kayal
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  2. Pascal Koiran
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  3. Timothée Pecatte
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  4. Chandan Saha
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Corresponding author

Correspondence to Chandan Saha .

Editor information

Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Kyoto University, Kyoto, Japan

    Kazuo Iwama

  3. The University of Tokyo, Tokyo, Japan

    Naoki Kobayashi

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Bettina Speckmann

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Kayal, N., Koiran, P., Pecatte, T., Saha, C. (2015). Lower Bounds for Sums of Powers of Low Degree Univariates. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47672-7_66

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  • DOI: https://doi.org/10.1007/978-3-662-47672-7_66

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47671-0

  • Online ISBN: 978-3-662-47672-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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