Lower bounds on arithmetic circuits via partial derivatives

Noam Nisan, Avi Wigderson

Research output: Contribution to journalArticlepeer-review

154 Scopus citations

Abstract

In this paper we describe a new technique for obtaining lower bounds on restricted classes of non-monotone arithmetic circuits. The heart of this technique is a complexity measure for multivariate polynomials, based on the linear span of their partial derivatives. We use the technique to obtain new lower bounds for computing symmetric polynomials (that hold over fields of characteristic zero) and iterated matrix products (that hold for all fields).

Original languageAmerican English
Pages (from-to)217-234
Number of pages18
JournalComputational Complexity
Volume6
Issue number3
DOIs
StatePublished - 1996

Keywords

  • Arithmetic circuits
  • Circuit complexity
  • Iterated matrix product
  • Lower bounds

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