Myhill-Nerode Theorem

The Myhill-Nerode Theorem provides a way to determine if a language (a set of strings) is regular—that is, can be recognized by a simple machine like a finite automaton. It states that a language is regular if and only if there are only a finite number of distinct "future behaviors" of its strings, meaning that strings can be grouped into a limited number of classes based on how they can be extended to produce valid strings. These classes, called equivalence classes, help in constructing the simplest possible automaton to recognize the language.