Nondeterministic unitary OBDDs

TL;DR

This paper analyzes the width complexity of nondeterministic unitary OBDDs, establishing lower bounds, comparing classical and quantum advantages, and exploring hierarchy and Boolean operation bounds.

Contribution

It introduces new lower bounds based on fooling sets, compares classical and quantum functions, and establishes a width hierarchy for NUOBDDs.

Findings

Lower bounds on NUOBDD widths using fooling sets

Classical functions that are hard for NUOBDDs and vice versa

Width hierarchy for NUOBDDs based on complexity

Abstract

We investigate the width complexity of nondeterministic unitary OBDDs (NUOBDDs). Firstly, we present a generic lower bound on their widths based on the size of strong 1-fooling sets. Then, we present classically cheap functions that are expensive for NUOBDDs and vice versa by improving the previous gap. We also present a function for which neither classical nor unitary nondeterminism does help. Moreover, based on our results, we present a width hierarchy for NUOBDDs. Lastly, we provide the bounds on the widths of NUOBDDs for the basic Boolean operations negation, union, and intersection.