Automata and Turing Machines

Abstract

In the 1930s, logicians (in particular Alan Turing and Alonzo Church) studied the meaning of computation as an abstract mental process and started to design theoretical devices to model it. As mentioned in the introduction, they needed a precise, formal definition of an algorithm in order to show that some of the problems posed by David Hilbert at the 1900 International Congress of Mathematicians could not be solved algorithmically. This was a very important step towards the construction of actual computers and, later, the design of programming languages. Turing machines influenced the development of digital computers, and the Lambda calculus is the basis of functional programming languages. At the same time, computers give to the early computability studies a practical application.