Bounds for Hodes - Specker theorem

  • Pavel Pudlák
Section VI: Complexity Of Boolean Functions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 171)


In [2] Hodes and Specker proved a theorem which implies that certain Boolean functions have nonlinear formula size complexity. I shall prove that the asymptotic bound for the theorem is n.log log n.


Boolean Function Binary Operation Boolean Formula Formula Size Symmetric Boolean Function 
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]
    M.J. Fischer, A.R. Meyer, M.S. Paterson: Ω (n log n) lower bounds on length of Boolean formulas, SIAM J. Comput. Vol. 11, No.3, 1982, 416–427.Google Scholar
  2. [2]
    L. Hodes, E. Specker: Lengths of formulas and elimination of quantifiers I, in Contributions to Mathematical Logic, H.A. Schmidt, K. Schütte, H.-J.Thiele, eds., North-Holland, (1968), 175–188.Google Scholar
  3. [3]
    V.M. Khrapčenko: On the complexity of the realization of the linear function in class of π-cirquits, Mat. Zametki 9, 1 (1971), 35–40, (Russian).Google Scholar
  4. [4]
    V.M. Khrapčenko: The complexity of realization of symmetrical functions by formulae, Mat. Zametki 11, 1 (1972), 109–120, (Russian), English translation in Math. Notes of the Academy of Sciences of the USSR 11, (1972), 70–76.Google Scholar
  5. [5]
    V.M. Khrapčenko: Complexity of realization of symmetric Boolean functions on finite basis, Problemy Kibernetiki 31, (1976), 231–234, (Russian).Google Scholar
  6. [6]
    R.E. Kričevskij: A bound for the formula size complexity of a Boolean function, Diskretny j Analiz I, (1963), 13–23, also in Dokl. Akad. Nauk SSSR, Vol. 151, No. 4, 803–806, (Russian), English translation in Sov. Phys.-Dokl., Vol. 8, No. 8, (1964), 770–772.Google Scholar
  7. [7]
    L. Lovász: Combinatorial Problems and Exercises, Akadémiai Kiadó and North-Holland, 1979.Google Scholar
  8. [8]
    E.I. Nečiporuk: A Boolean function, Dokl. Akad. Nauk SSSR, Vol. 169, No. 4, 765–766, (Russian), English translation in Sov. Math.-Dokl. Vol. 7, No. 4, (1966), 999–1000.Google Scholar
  9. [9]
    P. Pudlák: Boolean complexity and Ramsey theorems, manuscript.Google Scholar
  10. [10]
    J.E. Savage: The Complexity of Computing, John Wiley and Sons, (1976).Google Scholar
  11. [11]
    B. Vilfan: Lower bounds for the size of expressions for certain functions in d-ary logic, Theoretical Comp. Sci. 2, (1976), 249–269.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Pavel Pudlák
    • 1
  1. 1.Mathematical Institute ČSAVPrahaCzechoslovakia

Personalised recommendations