Where is finite automata decomposition used?

Question

Automation

Hello. Got a question. Where in the IT world are state machines used? And also the decomposition of finite automata? Where is it needed?

Answer 1

State machines are great for parsing a stream of input.

Answer 2

Cryptography.
For example, a stream encoder (generator of the so-called "gamma"): the transition function is a transitive 1-Lipschitz function, the output function is a balanced function.

Answer 3

Regular expressions are translated into the state machine. That is, whenever you work with regular expressions, your library compiles them into a state machine.