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On the complexity of branching programs and decision trees for clique functions

  • Ingo Wegener
Session CAAP 1 Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 249)

Abstract

Because of the slow progress in proving lower bounds on the circuit complexity of Boolean functions one is interested in restricted models of Boolean circuits like depth restricted circuits, decision trees, branching programs, width-k branching programs and k-times-only branching programs. We prove here exponentiallower bounds on the decision tree complexity of clique functions. For one-time-only branching programs we prove for k-clique functions large polynomial lower bounds if k is fixed and exponential lower bounds for k increasing with n. Finally we introduce the hierarchy of the classes BPk (P) of all sequences of Boolean functions which may be computed by k-times-only branching programs of polynomial size. We show constructively that BP1(P) is a proper subset of BP2(P).

Keywords

Decision Tree Boolean Function Turing Machine Disjunctive Normal Form Circuit Complexity 
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.

References

  1. [1]
    Ajtai,M./Babai,L./Hajnal,P./Komlós,M./Pudlák,P./Rödl,V./Szemerédi,E./Turán,G.: Two lower bounds for branching programs, 18. STOC, 30–38, 1986Google Scholar
  2. [2]
    Barrington,D.A.: Bounded-width polynomial-size branching programs recognize exactly those languages in NC1, 18.STOC,1–5, 1986Google Scholar
  3. [3]
    Borodin,A./Dolev,D./Fich,F.E./Paul,W.: Bounds for width two branching programs, 15.STOC, 87–93, 1983Google Scholar
  4. [4]
    Chandra,A.K./Furst,M.L./Lipton,R.J.: Multiparty protocols, 15.STOC, 94–99, 1983Google Scholar
  5. [5]
    Dunne, P.: Lower bounds on the complexity of 1-time only branching programs, FCT, LNCS 199, 90–99, 1985Google Scholar
  6. [6]
    Erdös,P./Kleitman,D.J./Rothschild,B.L.: Asymptotic enumeration of Kn-free graphs. Colloq.Intern.sulle Teorie Comb.,Accad.Naz. Lincei, Rome, 19–27, 1976Google Scholar
  7. [7]
    Kriegel,K./Waack,S.: Lower bounds on the complexity of real-time branching programs, Techn.Rep.,Akad.d.Wiss.Berlin (GDR), 1986Google Scholar
  8. [8]
    Masek,W.: A fast algorithm for the string editing problem and decision graph complexity, M.Sc. Thesis,MIT, 1976Google Scholar
  9. [9]
    Nechiporuk, E.I.: A Boolean function, Sov.Math.Dokl. 7, 999–1000, 1966Google Scholar
  10. [10]
    Pudlák, P.: A lower bound on complexity of branching programs, 11.MFCS,LNCS 176, 480–489, 1984Google Scholar
  11. [11]
    Pudlák,P./Zák,S.: Space complexity of computations, Preprint, Univ. Prague, 1983Google Scholar
  12. [12]
    Wegener, I.: Optimal decision trees and one-time-only branching programs for symmetric Boolean functions, Information and Control 62, 129–143, 1984CrossRefGoogle Scholar
  13. [13]
    Wegener,I.: On the complexity of branching programs and decision trees for clique functions, Techn.Rep.,Univ.Frankfurt a.M., 1984Google Scholar
  14. [14]
    Wegener, I.: Time-space trade-offs for branching programs, Journal of Computer and System Sciences 32, 91–96, 1986CrossRefGoogle Scholar
  15. [15]
    Yao, A.C.: Lower bounds by probabilistic arguments,24.FOCS, 420–428, 1983Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Ingo Wegener
    • 1
  1. 1.FB 20-InformatikJohann Wolfgang Goethe-UniversitätFrankfurt a.M.Fed.Rep. of Germany

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