Width Hierarchies for Quantum and Classical Ordered Binary Decision Diagrams with Repeated Test

Abstract

We consider quantum, nondterministic and probabilistic versions of known computational model Ordered Read-$k$-times Branching Programs or Ordered Binary Decision Diagrams with repeated test ($k$-QOBDD, $k$-NOBDD and $k$-POBDD). We show width hierarchy for complexity classes of Boolean function computed by these models and discuss relation between different variants of $k$-OBDD.

Submitted to RuFiDim 2017. arXiv admin note: substantial text overlap with arXiv:1703.00242, arXiv:1703.05015