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:
fn can be computed by polynomial size randomized read-once ordered branching program with a small one-sided error;
fn cannot be computed in polynomial size by deterministic read-once branching programs;
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
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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. https://doi.org/10.1007/3-540-61440-0_141
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