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Polynomial size test sets for commutative languages. (English) Zbl 0889.68091

Summary: 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 \(\Omega(n^2)\) is shown to exist.

MSC:

68Q45 Formal languages and automata
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References:

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