# Linear size test sets for certain commutative languages

Štěpán Holub; Juha Kortelainen

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 35, Issue: 5, page 453-475
- ISSN: 0988-3754

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topHolub, Štěpán, and Kortelainen, Juha. "Linear size test sets for certain commutative languages." RAIRO - Theoretical Informatics and Applications 35.5 (2010): 453-475. <http://eudml.org/doc/222009>.

@article{Holub2010,

abstract = {
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.
},

author = {Holub, Štěpán, Kortelainen, Juha},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {finite commutative language; word equations},

language = {eng},

month = {3},

number = {5},

pages = {453-475},

publisher = {EDP Sciences},

title = {Linear size test sets for certain commutative languages},

url = {http://eudml.org/doc/222009},

volume = {35},

year = {2010},

}

TY - JOUR

AU - Holub, Štěpán

AU - Kortelainen, Juha

TI - Linear size test sets for certain commutative languages

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 35

IS - 5

SP - 453

EP - 475

AB -
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.

LA - eng

KW - finite commutative language; word equations

UR - http://eudml.org/doc/222009

ER -

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