There Exist some Omega-Powers of Any Borel Rank
| dc.creator | Lecomte, Dominique | |
| dc.creator | Finkel, Olivier | |
| dc.date | 2007-06-25 | |
| dc.date.accessioned | 2026-07-07T09:26:01Z | |
| dc.date.available | 2026-07-07T09:26:01Z | |
| dc.description | Omega-powers of finitary languages are languages of infinite words (omega-languages) in the form V^omega, where V is a finitary language over a finite alphabet X. They appear very naturally in the characterizaton of regular or context-free omega-languages. Since the set of infinite words over a finite alphabet X can be equipped with the usual Cantor topology, the question of the topological complexity of omega-powers of finitary languages naturally arises and has been posed by Niwinski (1990), Simonnet (1992) and Staiger (1997). 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, that there exists a context free language L such that L^omega is analytic but not Borel, and that there exists a finitary language V such that V^omega is a Borel set of infinite rank. But it was still unknown which could be the possible infinite Borel ranks of omega-powers. We fill this gap here, proving the following very surprising result which shows that omega-powers exhibit a great topological complexity: for each non-null countable ordinal alpha, there exist some Sigma^0_alpha-complete omega-powers, and some Pi^0_alpha-complete omega-powers. | |
| dc.description | To appear in the Proceedings of the 16th EACSL Annual Conference on Computer Science and Logic, CSL 2007, Lausanne, Switzerland, September 11-15, 2007, Lecture Notes in Computer Science, (c) Springer, 2007 | |
| dc.identifier | https://arxiv.org/abs/0706.3523 | |
| dc.identifier | http://arxiv.org/abs/0706.3523 | |
| dc.identifier | Dans Proceedings of the 16th EACSL Annual Conference on Computer Science and Logic, CSL 2007, - 16th EACSL Annual Conference on Computer Science and Logic, CSL 2007, September 11-15, 2007, Lausanne : Suisse | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156608 | |
| dc.subject | Logic in Computer Science | |
| dc.subject | Computational Complexity | |
| dc.subject | Logic | |
| dc.title | There Exist some Omega-Powers of Any Borel Rank | |
| dc.type | text |