Randomization and nondeterminism are comparable for ordered read-onee branching programs

Abstract

In [3] we exhibited a simple boolean functions fn in n variables such that: fn can be computed by polynomial size randomized ordered read-once branching program with one sided small error; any nondeterministic ordered read-once branching program that computes fn has exponential size. In this paper we present a simple boolean function gn in n variables such that: gn can be computed by polynomial size nondeterministic ordered read-once branching program; any two-sided error randomized ordered read-once branching program that computes fn has exponential size.These mean that BPP and NP are incomparable in the context of ordered read-once branching program.