# Computational Limitations of Affine Automata

## TL;DR

This paper investigates the computational limits of affine automata, demonstrating their simulation in logarithmic space for certain cases and establishing impossibility results for algebraic-valued affine automata, thus delineating their recognition capabilities.

## Contribution

It provides new theoretical bounds on affine automata, including their simulation complexity and limitations in recognizing specific unary languages.

## Key findings

- Bounded-error rational-valued affine automata are simulated in logarithmic space.
- Algebraic-valued affine automata cannot recognize certain unary languages.
- Identifies limitations of affine automata with respect to recognition power.

## Abstract

We present two new results on the computational limitations of affine automata. First, we show that the computation of bounded-error rational-values affine automata is simulated in logarithmic space. Second, we give an impossibility result for algebraic-valued affine automata. As a result, we identify some unary languages (in logarithmic space) that are not recognized by algebraic-valued affine automata with cutpoints.