Automata Theory Essay

Discuss the application of automata theory to the practical parsing of programming languages and/or human languages. A good place to start is to read about LALR parsers and follow the trail from there.
Introduction
Automata theory is a theoretical branch of computer science. The word automation itself, represents processes that can be performed automatically without human interaction. Automata theory, is the study of what can possible be computed by these machines. Specifically, which problems can be solved through the use of machines. The goal is to find the simplest machine that can effectively preform a task, because this machine would most likely be the most efficient machine for that job as well.
Finite State Machines
The simplest category of machines is the finite state machine. Finite state machines are divided into

In theory a Turing Machine could be infinite, but in actual practice that would be impossible, because it would require a tape that is infinitely long. This is similar to the idea of having a computer with an infinite storage capacity. However, the machine first devised by Alan Turing in 1936, as a way to solve the Entscheindungsproblem. The Entscheindungsproblem was a famous mathematical problem formulated by David Hilbert. The problem asks if a formal language and a logical statement are provided, can an algorithm output either “True” or “False” based on its validity. It does not have to show how it got to that answer, but it does have to be always correct. Alan Turing and Alonzo Church ultimately proved that there was no answer to the problem, because there is no possible algorithm to decide whether statements in arithmetic are true or false. While he was not able to successfully prove the Entscheindungsproblem he was able to devise the first “infinite” machine, which modern computers would be based off. A Turing Machine can be represented mathematically as a seven-tuple