Linear size test sets for certain commutative languages
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 5, pp. 453-475.

We prove that for each positive integer n, the finite commutative language E n =c(a 1 a 2 a n ) possesses a test set of size at most 5n. Moreover, it is shown that each test set for E n has at least n-1 elements. The result is then generalized to commutative languages L containing a word w such that (i) alph(w)=alph(L); and (ii) each symbol aalph(L) occurs at least twice in w if it occurs at least twice in some word of L: each such L possesses a test set of size 11n, where n=Card(alph(L)). The considerations rest on the analysis of some basic types of word equations.

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     author = {Holub, \v{S}t\v{e}p\'an and Kortelainen, Juha},
     title = {Linear size test sets for certain commutative languages},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {453--475},
     publisher = {EDP-Sciences},
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     number = {5},
     year = {2001},
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     url = {http://www.numdam.org/item/ITA_2001__35_5_453_0/}
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Holub, Štěpán; Kortelainen, Juha. Linear size test sets for certain commutative languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 35 (2001) no. 5, pp. 453-475. http://www.numdam.org/item/ITA_2001__35_5_453_0/

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