Randomization and Nondeterminism Are Comparable for Ordered Read-Once Branching Programs

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. 1 Preliminaries Branching programs is well known model of computation for discrete functions 14]. Many types of restricted branching programs have been investigated as Work done in part while visiting Steklov Mathematical Institute in Moscow.