Rational set generalizes the notion ( of regular / rational language ) to monoids that are not necessarily Eilenberg's monograph often use either the term " recognizable language ", which refers to the behavior of automata, or " rational language ", which refers to important analogies between regular expressions and rational power series . ( In fact, Eilenberg defines rational and recognizable subsets of arbitrary monoids; the two notions do not, in general, coincide . ) This terminology, while better motivated, never really caught on, and " regular language " is used almost universally .
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Rational set generalizes the notion ( of regular / rational language ) to monoids that are not necessarily Eilenberg's monograph often use either the term " recognizable language ", which refers to the behavior of automata, or " rational language ", which refers to important analogies between regular expressions and rational power series . ( In fact, Eilenberg defines rational and recognizable subsets of arbitrary monoids; the two notions do not, in general, coincide . ) This terminology, while better motivated, never really caught on, and " regular language " is used almost universally .
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