Lower bounds for polynomial evaluation and interpolation problems

Victor Shoup, Roman Smolensky

Research output: Contribution to journalArticle

Abstract

We show that there is a set of points p1, p2, . . . , pn such that any arithmetic circuit of depth d for polynomial evaluation (or interpolation) at these points has size Ω (n log n/log(2 + d/log n)). Moreover, for circuits of sub-logarithmic depth d, we obtain a lower bound of Ω(dn1+1/d) on its size.

Original languageEnglish (US)
Pages (from-to)301-311
Number of pages11
JournalComputational Complexity
Volume6
Issue number4
DOIs
StatePublished - Jan 1 1996

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics(all)
  • Computational Theory and Mathematics
  • Computational Mathematics

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