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On Lower Bounds for Multiplicative Circuits and Linear Circuits in Noncommutative Domains

  • V. Arvind
  • S. Raja
  • A. V. Sreejith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8476)

Abstract

In this paper we show some lower bounds for the size of multiplicative circuits computing multi-output functions in some noncommutative domains such as monoids and finite groups. We also introduce and study a generalization of linear circuits in which the goal is to compute MY where Y is a vector of indeterminates and M is a matrix whose entries come from noncommutative rings. We show some lower bounds in this setting as well.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • V. Arvind
    • 1
  • S. Raja
    • 1
  • A. V. Sreejith
    • 2
  1. 1.The Institute of Mathematical Sciences (IMSc)ChennaiIndia
  2. 2.Tata Institute of Fundamental Research (TIFR)MumbaiIndia

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