How are automata theory and computer science connected through formal languages?

In automata theory, the connection between computer science and formal languages is established through the study of acceptors and generative grammars. This relationship allows researchers to classify computational power by matching specific types of automata with the complexity of the languages they can process.12

A generative grammar provides a finite set of rules used to produce the sentences of a language. In this framework, a language is defined as the set of all strings generated by these rules. Automata theory categorizes these systems based on their structural capabilities:1

• Finite-state acceptors: These are the simplest automata, which read input symbol by symbol. They correspond to finite-state grammars and are capable of recognizing "regular languages". While useful in information theory and neural network modeling, they are limited in their ability to handle complex phrase structures found in natural or standard computer languages.2
• Advanced acceptors: More complex automata, such as those with unbounded memory (e.g., the Turing machine), can recognize more sophisticated sets, including recursively enumerable sets.31

By defining languages through these formal rules, computer scientists can mathematically determine the limits of what a machine can compute, making these models fundamental to the development of computer architecture and programming languages.32