The Myhill-Nerode Theorem provides a necessary and sufficient condition for a formal language to be regular, characterizing regularity in terms of the number of equivalence classes formed by an equivalence relation defined on strings by their future behavior with respect to the language. Named for John Myhill and Anil Nerode, who proved it at the University of Chicago in 1957, it is a foundational result of automata theory used both to prove that particular languages are regular and, via the same equivalence classes, to construct the smallest possible deterministic finite automaton recognizing a given regular language.
Facts
StatementA language L is regular if and only if its Myhill-Nerode relation has a finite number of equivalence classes, and this number equals the number of states in the minimal deterministic finite automaton accepting L. 1 Classification
Statement Form Statement FormCharacterization Theorem 1 Connections
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Sources
1. Myhill-Nerode theorem (Wikipedia)
Statement
that this number is equal to the number of states in the minimal deterministic finite automaton (DFA) accepting L.
History
proved it at the University of Chicago in 1957
In Group: Computability and Complexity Theory, Lead section
In the theory of formal languages, the Myhill-Nerode theorem provides a necessary
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