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Trade-off between the Boolean and Arithmetic Depths of Modulo p Functions

  • Igor Shparlinski
Part of the Progress in Computer Science and Applied Logic book series (PCS, volume 17)

Abstract

For a polynomial f(X) ∈ ℤ[X] we consider Boolean functions producing the second leftmost bit of the smallest non-negative residues of f(x) modulo p from the bit representation of x and obtain a lower bound on their sensitivity (see Chapter 6 for the definition of this notion). Then a similar but a weaker bound is obtained for the sensitivity of Boolean functions producing the second leftmost bit of rational functions modulo p.

Keywords

Rational Function Boolean Function Unique Root Arithmetic Circuit Boolean Circuit 
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 Basel AG 1999

Authors and Affiliations

  • Igor Shparlinski
    • 1
  1. 1.School of Mathematics, Physics, Computing and ElectronicsMacquarie UniversityAustralia

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