Randomization and Nondeterminsm Are Incomparable 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 readonce 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. The research supported by Russia Fund for Basic Research 96-01-01962. i..