Issue |
RAIRO-Theor. Inf. Appl.
Volume 35, Number 5, September October 2001
|
|
---|---|---|
Page(s) | 453 - 475 | |
DOI | https://doi.org/10.1051/ita:2001105 | |
Published online | 15 August 2002 |
Linear size test sets for certain commutative languages
1
Turku Centre for Computer Science & Charles University, Prague, Czech
Republic
2
Department of Information Processing Science, University of Oulu, P.O. Box 3000,
90014 Oulun Yliopisto, Finland
Received:
April
2001
Accepted:
December
2001
We prove that for each positive integer n, the finite commutative language En = c(a1a2...an) possesses a test set of size at most 5n. Moreover, it is shown that each test set for En 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 11n, where n = Card(alph(L)). The considerations rest on the analysis of some basic types of word equations.
Mathematics Subject Classification: 68R15
© EDP Sciences, 2001
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