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Mathematics

Finite Automata and the Languages They Recognize

Quick fact

A finite automaton with n states can recognize a language that contains a string of length n only if there is a cycle, meaning that recognizing unbounded patterns requires some form of repetition.

Why this is interesting

Have you ever wondered how a vending machine knows you've inserted the right amount of money? It doesn't count every coin—it just remembers a few states. That's the essence of a finite automaton.