# Randomization and nondeterminism are comparable for ordered read-once branching programs

Session 3: Computational Complexity

First Online:

## Abstract

In [3] we exhibited a simple boolean functions

*f*_{ n }in*n*variables such that:- 1)
*f*_{ n }can be computed by polynomial size randomized ordered read-once branching program with one sided small error; - 2)
any nondeterministic ordered read-once branching program that computes

*f*_{ n }has exponential size.

In this paper we present a simple boolean function

*g*_{ n }in*n*variables such that:- 1)
*g*_{ n }can be computed by polynomial size nondeterministic ordered read-once branching program; - 2)
any two-sided error randomized ordered read-once branching program that computes

*f*_{ n }has exponential size.

These mean that *BPP* and *NP* are incomparable in the context of ordered read-once branching program.

## Keywords

Boolean Function Binary Decision Diagram Steklov Mathematical Institute Polynomial Size Exponential 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.

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