# Zero-Error Affine, Unitary, and Probabilistic OBDDs

## TL;DR

This paper introduces the affine OBDD model and demonstrates its exponential efficiency over traditional models in certain problems, along with quadratic improvements of Las Vegas models over deterministic ones.

## Contribution

It presents the affine OBDD model and compares its width to unitary, probabilistic, and deterministic OBDDs, revealing exponential and quadratic separations.

## Key findings

- Zero-error affine OBDDs can be exponentially narrower.
- Las Vegas unitary and probabilistic OBDDs can be quadratically narrower.
- Results hold for automata versions of these models.

## Abstract

We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results by considering the automata versions of these models.