# One-Way Topological Automata and the Tantalizing Effects of Their Topological Features

## TL;DR

This paper introduces a generalized model of one-way deterministic topological automata that evolves configurations in topological spaces, exploring how different topological features influence their language recognition capabilities.

## Contribution

It proposes a new, flexible automata model that unifies various automata types and analyzes the impact of topological features on their computational power.

## Key findings

- Automata can recognize a broader class of languages with topological features.
- Different topological spaces and maps significantly affect automata behavior.
- The model generalizes finite, probabilistic, quantum, and pushdown automata.

## Abstract

We cast new light on the existing models of one-way deterministic topological automata by introducing a fresh but general, convenient model, in which, as each input symbol is read, an interior system of an automaton, known as a configuration, continues to evolve in a topological space by applying continuous transition operators one by one. The acceptance and rejection of a given input are determined by observing the interior system after the input is completely processed. Such automata naturally generalize one-way finite automata of various types, including deterministic, probabilistic, quantum, and pushdown automata. We examine the strengths and weaknesses of the power of this new automata model when recognizing formal languages. We investigate tantalizing effects of various topological features of our topological automata by analyzing their behaviors when different kinds of topological spaces and continuous maps, which are used respectively as configuration spaces and transition operators, are provided to the automata. Finally, we present goals and directions of future studies on the topological features of topological automata.