On BPP versus NP ∪ coNP for ordered read-once branching programs

We investigate the relationship between probabilistic and nondeterministic complexity classes PP, BPP, NP and coNP with respect to ordered read-once branching programs (OBDDs). We exhibit two explicit Boolean functions qn,Rn such that: (1) qn:{0, 1}n → {0, 1} belongs to BPP\(NP ∪ coNP) in the context of OBDDs; (2) Rn:{0, 1}n → {0, 1} belongs to PP\(BPP ∪ NP ∪ coNP) in the context of OBDDs. Both of these functions are not in AC0. © 2001 Elsevier Science B.V. All rights reserved