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Lower bounds for polynomial evaluation and interpolation problems

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Abstract

We show that there is a set of pointsp 1,p 2,...,p n such that any arithmetic circuit of depthd for polynomial evaluation (or interpolation) at these points has size

$$\Omega \left( {\frac{{n\log n}}{{\log (2 + d/\log n}}} \right).$$

Moreover, for circuits of sub-logarithmic depthd, we obtain a lower bound of Ω(dn 1+1/d) on its size.

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Authors and Affiliations

  1. IBM Zürich Research Laboratory, Säumerstraße 4, 8803, Rüschlikon, Switzerland

    Victor Shoup

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  1. Victor Shoup
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  2. Roman Smolensky
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Dedicated to the memory of Roman Smolensky

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Shoup, V., Smolensky, R. Lower bounds for polynomial evaluation and interpolation problems. Comput Complexity 6, 301–311 (1996). https://doi.org/10.1007/BF01270384

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  • DOI: https://doi.org/10.1007/BF01270384

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