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Linear size test sets for certain commutative languages

Published online by Cambridge University Press:  15 August 2002

Štěpán Holub  and
Juha Kortelainen
Štěpán Holub
Affiliation:
Turku Centre for Computer Science & Charles University, Prague, Czech Republic Department of Information Processing Science, University of Oulu, P.O. Box 3000, 90014 Oulun Yliopisto, Finland
Juha Kortelainen
Affiliation:
Turku Centre for Computer Science & Charles University, Prague, Czech Republic Department of Information Processing Science, University of Oulu, P.O. Box 3000, 90014 Oulun Yliopisto, Finland
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Abstract

We prove that for each positive integer n, the finite commutative languageEn = c(a 1 a 2...an ) 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 ∈ 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.

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Type
Research Article
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RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 5 , September 2001 , pp. 453 - 475
Copyright
© EDP Sciences, 2001

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