On Recognizable Languages of Infinite Pictures
| dc.creator | Finkel, Olivier | |
| dc.date | 2009-01-24 | |
| dc.date.accessioned | 2026-07-07T12:34:23Z | |
| dc.date.available | 2026-07-07T12:34:23Z | |
| dc.description | In a recent paper, Altenbernd, Thomas and Wöhrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the Büchi and Muller ones, firstly used for infinite words. The authors asked for comparing the tiling system acceptance with an acceptance of pictures row by row using an automaton model over ordinal words of length $ω^2$. We give in this paper a solution to this problem, showing that all languages of infinite pictures which are accepted row by row by Büchi or Choueka automata reading words of length $ω^2$ are Büchi recognized by a finite tiling system, but the converse is not true. We give also the answer to two other questions which were raised by Altenbernd, Thomas and Wöhrle, showing that it is undecidable whether a Büchi recognizable language of infinite pictures is E-recognizable (respectively, A-recognizable). | |
| dc.description | An erratum is added at the end of the paper: The supremum of the set of Borel ranks of Büchi recognizable languages of infinite pictures is not the first non recursive ordinal $ω_1^{CK}$ but an ordinal $γ^1_2$ which is strictly greater than the ordinal $ω_1^{CK}$. This follows from a result proved by Kechris, Marker and Sami (JSL 1989) | |
| dc.identifier | https://arxiv.org/abs/0901.3828 | |
| dc.identifier | http://arxiv.org/abs/0901.3828 | |
| dc.identifier | International Journal of Foundations of Computer Science 15, 6 (2004) 823-840 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217414 | |
| dc.subject | Logic in Computer Science | |
| dc.subject | Computational Complexity | |
| dc.subject | Logic | |
| dc.title | On Recognizable Languages of Infinite Pictures | |
| dc.type | text |