Máquina de Turing como transdutor de operações aritméticas fundamentais

Abstract

The Turing Machine is recognized as the main theoretical foundation responsible for the development of digital computers; it is a formal framework that models the way problems could be solved by a person. This work presents Turing Machines implemented as transducers of fundamental arithmetic operations, performing the four basic arithmetic operations of addition, subtraction, multiplication and division, from their simplest form with one-digit numbers, to the most elaborate composition of algorithms involving multi-digit numbers. The most important issue is to demonstrate how, from an eminently symbolic structure, it can be constructed in order to perform fundamental mathematical operations, which can be extrapolated to solve even more complex issues. In this way, it is demonstrated how a machine with limited capacity to read, recognize and print symbols can be used to perform arithmetic operations, as seen in machines that are considered more powerful, such as current calculators and computers. It is hoped that the content of this work will establish a bridge between the theoretical concepts of TMs and their historical descendants, digital computers, in solving the most diverse problems.