On the computational power of affine automata

TL;DR

This paper explores the computational capabilities of affine automata, providing new methods for error reduction and demonstrating limitations by identifying languages they cannot recognize with bounded error.

Contribution

It offers a simplified proof for cutpoint adjustment, introduces a technique to reduce error, and shows certain languages are beyond affine automata's recognition power.

Findings

A method to change the cutpoint for affine automata

A technique to reduce error in bounded-error affine automata

Identification of languages not recognized by affine automata with bounded error

Abstract

We investigate the computational power of affine automata (AfAs) introduced in [4]. In particular, we present a simpler proof for how to change the cutpoint for any affine language and a method how to reduce error in bounded error case. Moreover, we address to the question of [4] by showing that any affine language can be recognized by an AfA with certain limitation on the entries of affine states and transition matrices. Lastly, we present the first languages shown to be not recognized by AfAs with bounded-error.