Abstract
It is proved that any commutative language over an alphabet of n symbols possesses a test set of size O (n 2 ). If the Parikh-map of the language is a linear set, then the minimum size of the test set is O (n log n). A finite commutative language over an alphabet of n symbols such that the smallest test set for the language is of size Ω (n 2 ) is shown to exist.
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