computational complexity

, Volume 6, Issue 3, pp 217–234

Lower bounds on arithmetic circuits via partial derivatives

  • Noam Nisan
  • Avi Wigderson

DOI: 10.1007/BF01294256

Cite this article as:
Nisan, N. & Wigderson, A. Comput Complexity (1996) 6: 217. doi:10.1007/BF01294256


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).

Key words

Circuit complexity arithmetic circuits lower bounds iterated matrix product 

Subject classifications

68Q25 68Q40 
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Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Noam Nisan
    • 1
  • Avi Wigderson
    • 1
  1. 1.Institute of Computer ScienceThe Hebrew University of JerusalemIsrael

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