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Cancellation-Free Circuits in Unbounded and Bounded Depth

  • Joan Boyar
  • Magnus Gausdal Find
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8070)

Abstract

We study the notion of “cancellation-free” circuits. This is a restriction of linear Boolean circuits (XOR-circuits), but can be considered as being equivalent to previously studied models of computation. The notion was coined by Boyar and Peralta in a study of heuristics for a particular circuit minimization problem. They asked how large a gap there can be between the smallest cancellation-free circuit and the smallest linear circuit. We show that the difference can be a factor Ω(n/log2 n). This improves on a recent result by Sergeev and Gashkov who have studied a similar problem. Furthermore, our proof holds for circuits of constant depth. We also study the complexity of computing the Sierpinski matrix using cancellation-free circuits and give a tight Ω(nlogn) lower bound.

Keywords

Boolean Function Constant Depth Hadamard Matrice Strong Separation Nonzero Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Joan Boyar
    • 1
  • Magnus Gausdal Find
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkDenmark

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