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Journal of Automata, Languages and Combinatorics
formerly:
Journal of Information Processing and Cybernetics /
Elektronische Informationsverarbeitung und Kybernetik
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@article{jalc010102,
author = {Lila Kari and Gabriel Thierrin},
title = {Omega-Syntactic Congruences},
journal = jalc,
year = 1996,
volume = 1,
number = 1,
pages = {13--26},
keywords = {$\omega$-syntactic congruence, $\omega$-language,
dense language, disjunctive language, residue,
syntactic monoid},
abstract = {An $\omega$-language over a finite alphabet $X$ is a set
of infinite sequences of letters of $X$. Previously studied
syntactic equivalence relations defined by
$\omega$-languages have mainly been relations on $X^*$.
In this paper the emphasis is put on relations in
$X^{\omega}$, by associating to an $\omega$-language $L$ a
congruence on $X^{\omega}$, called the $\omega$-syntactic
congruence of $L$. Properties of this congruence and
notions induced by it, such as $\omega$-residue,
$\omega$-density, and separativeness are defined and
investigated. Finally, a congruence on $X^*$ related to the
$\omega$-syntactic congruence and quasi-orders on
$X^{\omega}$ induced by an $\omega$-language are studied.}
}