Mathematical Approach in Automata and Automata Association

TL;DR

This paper explores a mathematical framework for automata using topology and measure theory, enabling simplified analysis of complex automata systems through advanced mathematical structures.

Contribution

It introduces a novel topological and measure-theoretic approach to automata, providing new tools for analyzing automata systems mathematically.

Findings

Automata states can be modeled as topological spaces.

Probabilistic automata can be represented using measure theory.

Mathematical structures simplify the analysis of complex automata systems.

Abstract

The transition structure of an automaton can be used to create a natural topology to the set of states of an automaton, generating, this way, a topological space. Probabilistic automata can also be modeled in terms of measure theory. A system of many automata would be reduced to simple mathematical structures and analyzed by a topological point of view.