Sharpening an upper bound on the adder and comparator depths



The upper bound log2 n + log2 log2 n + const is proved on the depth of the addition and comparison operators on n-bit numbers over the basis {&, ∨, ∼}.


Industrial Mathematic Boolean Function Inductive Assumption Essential Variable Depth 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. B. Gashkov, M. I. Grinchuk, and I. S. Sergeev, “Circuit Design of an Adder of Small Depth,” Diskret. Anal. Issl. Oper., Ser. 1, 14(1), 27–44 (2007) [J. Appl. Industr. Math. 2 (2), 167–178 (2008)].MathSciNetGoogle Scholar
  2. 2.
    O. B. Lupanov, Asymptotic Estimates for the Complexity of Control Systems (Moskov. Gos. Univ., Moscow, 1984) [in Russian].Google Scholar
  3. 3.
    N. P. Red’kin, “On the Minimal Realization of a Binary Adder,” Problemy Kibernet. 38, 181–216 (1981).MathSciNetGoogle Scholar
  4. 4.
    V. M. Khrapchenko, “Asymptotic Estimation of the Addition Time of a Parallel Adder,” Problemy Kibernet. 19, 107–122 (1967) [Syst. Theory Res. 19, 105–122 (1970)].Google Scholar
  5. 5.
    V. M. Khrapchenko, “On Possibility of Refining Bounds for the Delay of a Parallel Adder,” Diskret. Anal. Issl. Oper., Ser. 1, 14(1), 87–93 (2007) [J. Appl. Industr. Math. 2 (2), 211–214 (2008)].MathSciNetGoogle Scholar
  6. 6.
    S. B. Gashkov, A. E. Andreev, and A. Lu, “Optimization of Comparator Architecture,” US Patent No. 6691283 (February 10, 2004).Google Scholar
  7. 7.
    S. B. Gashkov, A. E. Andreev, and A. Lu, “Optimization of Adder Based Circuit Architecture,” US Patent No. 6934733 (August 23, 2005).Google Scholar
  8. 8.
    M. I. Grinchuk, “Low Depth Circuit Design,” US Patent Appl. (2008).Google Scholar
  9. 9.
    M. I. Grinchuk and A. A. Bolotov, “Process for Designing Comparators and Adders of Small Depth,” US Patent No. 7020865 (March 28, 2006).Google Scholar
  10. 10.
    J. E. Savage, The Complexity of Computing (Wiley, New York, 1976).MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia

Personalised recommendations