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On the power of randomized branching programs

Session 8: Complexity Theory

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1099)


We define the notion of a randomized branching program in the natural way similar to the definition of a randomized circuit. We exhibit an explicit function f n for which we prove that:

  1. 1)

    fn can be computed by polynomial size randomized read-once ordered branching program with a small one-sided error;

  2. 2)

    fn cannot be computed in polynomial size by deterministic read-once branching programs;

  3. 3)

    fn cannot be computed in polynomial size by deterministic read-κ-times ordered branching program for k = o(n/log n) (the required deterministic size is exp (Ω (n/k))).


  • Boolean Function
  • Random Oracle
  • Random Input
  • Polynomial Size
  • Communication Game

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.

Research partially supported by the Volkswagen-Stiftung and the Basic Research Grant 96-01-01962

Research partially supported by DFG Grant K A 673/4-1, by the ESPRIT BR Grants 7097 and EC-US 030, and by the Volkswagen-Stiftung.

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Ablayev, F., Karpinski, M. (1996). On the power of randomized branching programs. In: Meyer, F., Monien, B. (eds) Automata, Languages and Programming. ICALP 1996. Lecture Notes in Computer Science, vol 1099. Springer, Berlin, Heidelberg.

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