A superpolynomial lower bound for (1,+k(n))-branching programs

  • Stanislav Žák
Contributed Papers Lower Bounds
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)


By (1,+k(n))-branching programs (b. p.s) we mean those b. p.s which during each of their computations are allowed to test at most k(n) input bits repeatedly. For a Boolean function J computable within polynomial time a trade-off has been proven between the number of repeatedly tested bits and the size of each b. p. P which computes J. If at most ≫√n/48(log(c(n)))2⌋ — 1 repeated tests are allowed then the size of P is at least c(n). This yields superpolynomial lower bounds for e. g. (1, +√n/48(log(n)loglog(n))2) -b. p.'s and for (1, +√n/48(log(n))4)-b. p.'s.

The presented result is a step towards a superpolynomial lower bound for 2-b. p.'s which is an open problem since 1984 when the first superpolynomial lower bounds for 1-b. p.s were proven [6], [7].


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  1. [1]
    A. Borodin, A.Razborov, R. Smolensky-On Lower Bounds for Read-k-times Branching Programs — Computational Complexity 3,1–18.Google Scholar
  2. [2]
    S. Jukna-A Note on Read-k-times Branching Programs-Universität Dortmund-Forschungsbericht Nr. 448, 1992Google Scholar
  3. [3]
    M. Ftáčnik, J. Hromkovič-Nonlinear Lower Bound for Real-Time Branching Programs.Google Scholar
  4. [4]
    K. Kriegel, S. Waack-Exponential Lower Bounds for Real-time Branching Programs-Proc. FCT'87, LNCS 278, 263–267.Google Scholar
  5. [5]
    D. Sieling-New Lower Bounds and Hierarchy Results for Restricted Branching ProgramsGoogle Scholar
  6. [6]
    I. Wegener-On the Complexity of Branching Programs and Decision Trees for Clique Functions-JACM 35, 1988, 461–471.CrossRefGoogle Scholar
  7. [7]
    S. Žák-An Exponential Lower Bound for One-time-only Branching Programs-MFCS'84, LNCS 176, 562–566.Google Scholar
  8. [8]
    S. Žák-An Exponential Lower Bound for Real-time Branching Programs-Information and Control, Vol. 71, No 1/2, 87–94.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Stanislav Žák
    • 1
  1. 1.Institute of Computer ScienceAcademy of Sciences of the Czech RepublicPrague 8Czech Republic

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