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Article Dans Une Revue Fundamenta Informaticae Année : 2004

An omega-Power of a Finitary Language Which is a Borel Set of Infinite Rank

Olivier Finkel
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Résumé

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.
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Dates et versions

hal-00108219 , version 1 (20-10-2006)
hal-00108219 , version 2 (03-01-2008)

Identifiants

  • HAL Id : hal-00108219 , version 1

Citer

Olivier Finkel. An omega-Power of a Finitary Language Which is a Borel Set of Infinite Rank. Fundamenta Informaticae, 2004, 62 (3-4), pp.333-342. ⟨hal-00108219v1⟩
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