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

TL;DR

This paper establishes width hierarchies for quantum, nondeterministic, and probabilistic ordered binary decision diagrams with repeated tests, revealing their computational complexity relationships.

Contribution

It introduces width hierarchy results for various $k$-OBDD models and analyzes the relationships among their different variants.

Findings

Width hierarchies are established for $k$-QOBDD, $k$-NOBDD, and $k$-POBDD.

Relations between different $k$-OBDD variants are discussed.

The results clarify the computational power differences among these models.

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.