Restricted branching programs and their computational power

Invited Lectures
Part of the Lecture Notes in Computer Science book series (LNCS, volume 452)


In order to acquire insight about arbitrary branching programs, a number of restricted branching program models have been considered. Among these are decision trees, read-once-only branching programs length-restricted oblivious branching programs and width-restricted branching programs. In the following we survey some results which characterize the computational power of such restricted models. Interestingly, we are able to establish strong differences in the computational power of deterministic, nondeterministic, parity, or alternating restricted branching programs for most of the mentioned types. For details we refer to [Me89].


Boolean Function Computational Power Turing Machine Complexity Class Polynomial Size 
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. [A&86]
    M.Ajtai, L.Babai, P.Hajnal, J.Komlos, P.Pudlak, V.Rödl, E.Szemeredi G.Turan: Two Lower Bounds for Branching Programs, Proc. 18.ACM STOC (1986), 30–38.Google Scholar
  2. [An85]
    A.E.Andreev: On a Method of Obtaining Lower Bounds for the Complexity of Individual Montone Functions, Dokl. Akad. Nauk SSSR 282/5, 1033–1037.Google Scholar
  3. [Ba86]
    D.A.Barrington: Bounded-width Polynomial Size Branching Programs Recognize Exactly those Languages in NC1, Proc. 18. ACM STOC, 1–5.Google Scholar
  4. [Co66]
    A.Cobham: The Recognition Problem for the Set of Perfect Squares, Research paper RC-1704, IBM Watson Research Centre, 1966.Google Scholar
  5. [DM89]
    C.Damm, Ch.Meinel: Separating Completely Complexity Classes Related to Polynomial Size Ω-Decision Trees, Proc. FCT'89, LNCS 380, 127–136.Google Scholar
  6. [FSS81]
    M.Furst, J.B.Saxe, M.Sipser: Parity, Circuits, and the Polynomial Time Hierarchy, Proc. 22. IEEE FOCS, 1981, 260–270.Google Scholar
  7. [Ha86]
    J.Hastad: Improved Lower Bounds for Small Depth Circuits, Proc. 18.ACM STOC (1986), 6–20.Google Scholar
  8. [Im87]
    N.Immerman: Nondeterministic Space is Closed Under Complement, Techn. Report 552, Yale Univ., 1987.Google Scholar
  9. [KL80]
    R.M.Karp, R.J.Lipton: Some Connections Between Nonuniform and Uniform Complexity Classes, Proc. 12.ACM STOC (1980), 302–309.Google Scholar
  10. [KW87]
    K.Kriegel, S.Waack: Exponential Lower Bounds for Real-time Branching Programs, Proc. FCT'87, LNCS 278, 263–267.Google Scholar
  11. [Kr90]
    M.Krause: Separating ⊕L from L, NL, co-NL, and AL for oblivious Turing Machines of Linear Access-Time, This volume.Google Scholar
  12. [KMW88]
    M.Krause, Ch.Meinel, S.Waack: Separating the Eraser Turing Machine Classes L e, NL e, co-NL e and P e, Proc. MFCS'88, LNCS 324, 405–413.Google Scholar
  13. [KMW89]
    M.Krause, Ch.Meinel, S.Waack: Separating Complexity Classes Related to Restricted Logarithmic Space-Bounded Turing Machines, Proc. 4th Structure in Complexity Theory (Eugene, USA), 240–259.Google Scholar
  14. [Le59]
    C.Y. Lee: Representation of Switching Functions by Binary Decision Programs, Bell System Techn. Journal 38 (1959), 985–999.Google Scholar
  15. [Ma76]
    W.Masek: A Fast Algorithm for the String Editing Problem and Decision Graph Complexity, M.Sc. thesis, MIT, 1976.Google Scholar
  16. [Me86]
    Ch.Meinel: P-projection Reducibility and the Complexity Classes L(nonuniform) and NL(nonuniform), Proc. MFCS'86, LNCS 233, 527–535.Google Scholar
  17. [Me87]
    Ch.Meinel: The Power of Nondeterminism in Polynomial-size Bounded-width Branching Programs, Proc. FCT'87, LNCS 278, 302–309.Google Scholar
  18. [Me88]
    Ch.Meinel: The Power of Polynomial Size Ω-branching Programs, Proc. STACS'88, Bordeaux, LNCS 294, 81–90.Google Scholar
  19. [Me89]
    Ch.Meinel: Modified branching Programs and their Computational Power, (Habilitation Thesis) LNCS 370.Google Scholar
  20. [Ne66]
    E.I.Nechiporuk: A Boolean Function, Sov. Math. Dokl., No.7, 1966, 999–1000.Google Scholar
  21. [Po21]
    E. Post: Introduction to a General Theory of Elementary Propositions, Am. J. Math. 43 (1921), 163–185.Google Scholar
  22. [Pu84]
    P.Pudlak: A Lower Bound on Complexity of Branching Programs, Proc. MFCS'84, LNCS 176, 480–489.Google Scholar
  23. [PŽ83]
    P.Pudlak, S.Žak: Space Complexity of Computations, Preprint Univ. of Prague, 1983.Google Scholar
  24. [Ra85]
    A.A.Razborov: A Lower Bound for the Monotone Network Complexity of the Logical Permanent, Matem. Zametki 37/6.Google Scholar
  25. [Ra86]
    A.A.Razborov: Lower Bounds on the Size of Bounded-depth Networks over the Basis {#x22C0;,⊕}, Techn. Preprint Steklov Inst. Moskau, 1986.Google Scholar
  26. [Ru81]
    W. Ruzzo: On Uniform Circuit Complexity, JCSS 22 (3), 1981, 236–283.Google Scholar
  27. [Sz87]
    R. Szelepcsenyi: The Method of Forcing for Nondeterministic Automata, Bull. EATCS 33, 96–99, 1987.Google Scholar
  28. [We84]
    I.Wegener: Optimal Decision Trees and 1-Time Only Branching Programs for Symmetric Boolean Functions, Proc. 9th CAAP, 1984.Google Scholar
  29. [We88]
    I. Wegener: On the Complexity of Branching Programs and Decision Trees for Clique Functions, JACM Vol. 35, No. 2 (1988), 461–471.Google Scholar
  30. [Ya85]
    A.C.Yao: Separating the Polynomial-time hierarchy by Oracles, Proc. 26.IEEE FOCS (1985), 1–10.Google Scholar
  31. [Ža84]
    S.Žak: An Exponential Lower Bound for One-time-only Branching Programs, Proc. MFCS'84, LNCS 176, 562–566.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  1. 1.Sektion Informatik Humboldt-Universität zu BerlinBerlin

Personalised recommendations