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Abstract: We prove that for each positive integer n; the nite 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 a 2 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 11n, where n =... (Update)
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BibTeX entry: (Update)
@misc{ holub-linear,
author = "Stepan Holub and Juha Kortelainen",
title = "Linear Size Test Sets for Certain Commutative Languages",
url = "citeseer.ist.psu.edu/holub01linear.html" }
Citations (may not include all citations):44 A combinatorial problem in geometry (context) - Erd, Szekeres - 1935
24 Combinatorics on words (context) - Cho, Karhum - 1997
11 A proof of Ehrenfeucht`s conjecture (context) - Albert, Lawrence - 1985
4 On binary equality sets and a solution to the test set conje.. (context) - Ehrenfeucht, Karhum et al. - 1983
2 On word equations and the morphism equivqalence problem for .. (context) - Hakala - 1968
1 maximal extensions and their effective constructions (context) - Albert, sets et al. - 1968
1 test sets rich languages and commutatively closed languages (context) - Albert, Wood et al. - 1983
1 Linear size test sets for commutative languages (context) - Hakala, Kortelainen - 1997
1 the system of word equations (context) - Hakala, Kortelainen
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