On the homomorphism between Formal Neural Nets and Automata

Historically the concept of artificial neural nets was born from the efforts to formalize the properties of the nervous system according to the mathematical and logical tools available at the time. After the pioneering work by McCulloch and Pitts in 1943, A Logical Calculus of the Ideas Immanent in Nervous Activity that is one of the most important work in this field, the theoretical frame casted by them was taken over by several theorists of various scientific fields. Here was born the interplay between neurophysiology, computer science, biology, physics, logic, mathematics, probability and the concept of Biocobernetic.

Mathematical analysis has solved some of the mysteries posed by the new models but has left many questions open for future investigations. Needless to say, the study of neurons, their interconnections, and their role as the brain elementary building blocks is one of the most dynamic and important research fields in modern biology.

Mathematics, physics, and computer science can provide invaluable help in the study of these complex systems. It is not surprising that the study of the brain has become one of the most interdisciplinary areas of scientific research in recent years.
In 60s and 70s computational theorists gave rise to the algebraic theory of automata as an extension to the models of computations proposed until that.

In theoretical computer science, automata theory is the study of abstract machines, that are models of computer hardwares and softwares, and the computational problems that can be solved using these machines.

This thesis aims to explain the relationship between Artificial Neural Nets and Automata Theory, pointing out the historical evolutions and the possible applications.
In Chapter 1 an introduction about McCulloch and Pitts model for neurons and Formal Neural Nets (FNN) (that are a natural extension of the last one) are gived.
In Chapter 2 models of neural nets with loops and an introduction to Automata Theory are presented.
In Chapter 3 Theorems that define the homomorphism between FNN and finite automata are provided.
In Chapter 4 problems about stability and oscillation of a net are presented.
In Chapter 5 a practical application in robotics is developed.

This thesis was written in the last Academic Year, during the period spent at the University of Las Palmas de Gran Canaria, for the Erasmus project, under the guidance of the professor Roberto Moreno Diaz and the professor Gabriel De Blasio of the Instituto Universitario De Ciencias y Tecnologías Cibernética.