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Linear size test sets for certain commutative languages

Štěpán HolubJuha Kortelainen — 2001

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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 5 n . 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 a alph ( 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 11 n , where n = Card ( alph ( L ) ) . The considerations rest on the analysis of some basic types of word equations....

Linear size test sets for certain commutative languages

Štěpán HolubJuha Kortelainen — 2010

RAIRO - Theoretical Informatics and Applications

We prove that for each positive integer the finite commutative language = ( ...) possesses a test set of size at most Moreover, it is shown that each test set for has at least -1 elements. The result is then generalized to commutative languages containing a word such that (i) alph() = alph}(); and (ii) each symbol ∈ alph}() occurs at least twice in if it occurs at least twice in some word of : each such possesses a test set...

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