# On the power of randomized branching programs

Session 8: Complexity Theory

First Online:

## 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-κ-times ordered branching program for*k*= o(*n*/log*n*) (the required deterministic size is exp (Ω (*n/k*))).

## Keywords

Boolean Function Random Oracle Random Input Polynomial Size Communication Game
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