## On the Power of Randomized Branching Programs

### Authors: Farid Ablayev, Marek Karpinski

ABSTRACT

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) $f_{n}$ can be computed by polynomial size randomized read-once ordered branching program with a small one-sided error;

2) $f_{n}$ cannot be computed in polynomial size by deterministic read-once branching programs;

3) $f_{n}$ cannot be computed in polynomial size by deterministic read-$k$-times ordered branching program for $k=o(n/\log n)$ (the required deterministic size is $\exp\left(\Omega\left(\frac{n}{k}\right)\right)$).

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1996/96-46.ps.gz

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