Omega-powers of finitary languages are omega languages in the form V^omega, where V is a finitary language over a finite alphabet X. Since the set of infinite words over X can be equipped with the usual Cantor topology, the question of the topological complexity of omega-powers naturally arises and has been raised by Niwinski, by Simonnet, and by Staiger. It has been recently proved that for each integer n > 0 , there exist some omega-powers of context free languages which are Pi^0_n-complete Borel sets, and that there exists a context free language L such that L^omega is analytic but not Borel. But the question was still open whether there exists a finitary language V such that V^omega is a Borel set of infinite rank. We answer this question in this paper, giving an example of a finitary language whose omega-power is Borel of infinite rank.
Publié le : 2004-07-05
Classification:
Infinite words,
omega-languages,
omega-powers,
Cantor topology,
topological complexity,
Borel sets,
infinite rank,
[INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO],
[MATH.MATH-LO]Mathematics [math]/Logic [math.LO]
@article{hal-00108219,
author = {Finkel, Olivier},
title = {An omega-Power of a Finitary Language Which is a Borel Set of Infinite Rank},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00108219}
}
Finkel, Olivier. An omega-Power of a Finitary Language Which is a Borel Set of Infinite Rank. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00108219/