On Recognizable Languages of Infinite Pictures
In a recent paper, Altenbernd, Thomas and W\"ohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\"uchi and Muller ones, firstly used for infinite words. The authors...
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fttriple:oai:gotriple.eu:10670/1.ve2m4b 2023-05-15T18:12:35+02:00 On Recognizable Languages of Infinite Pictures Finkel, Olivier 2009-01-24 http://arxiv.org/abs/0901.3828 en eng International Journal of Foundations of Computer Science 15, 6 (2004) 823-840 10670/1.ve2m4b http://arxiv.org/abs/0901.3828 undefined arXiv phil psy Text https://vocabularies.coar-repositories.org/resource_types/c_18cf/ 2009 fttriple 2023-01-22T17:26:34Z In a recent paper, Altenbernd, Thomas and W\"ohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\"uchi 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 $\omega^2$. We give in this paper a solution to this problem, showing that all languages of infinite pictures which are accepted row by row by B\"uchi or Choueka automata reading words of length $\omega^2$ are B\"uchi 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 W\"ohrle, showing that it is undecidable whether a B\"uchi recognizable language of infinite pictures is E-recognizable (respectively, A-recognizable). Comment: An erratum is added at the end of the paper: The supremum of the set of Borel ranks of B\"uchi recognizable languages of infinite pictures is not the first non recursive ordinal $\omega_1^{CK}$ but an ordinal $\gamma^1_2$ which is strictly greater than the ordinal $\omega_1^{CK}$. This follows from a result proved by Kechris, Marker and Sami (JSL 1989) Text sami Unknown |
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phil psy Finkel, Olivier On Recognizable Languages of Infinite Pictures |
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In a recent paper, Altenbernd, Thomas and W\"ohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the B\"uchi 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 $\omega^2$. We give in this paper a solution to this problem, showing that all languages of infinite pictures which are accepted row by row by B\"uchi or Choueka automata reading words of length $\omega^2$ are B\"uchi 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 W\"ohrle, showing that it is undecidable whether a B\"uchi recognizable language of infinite pictures is E-recognizable (respectively, A-recognizable). Comment: An erratum is added at the end of the paper: The supremum of the set of Borel ranks of B\"uchi recognizable languages of infinite pictures is not the first non recursive ordinal $\omega_1^{CK}$ but an ordinal $\gamma^1_2$ which is strictly greater than the ordinal $\omega_1^{CK}$. This follows from a result proved by Kechris, Marker and Sami (JSL 1989) |
format |
Text |
author |
Finkel, Olivier |
author_facet |
Finkel, Olivier |
author_sort |
Finkel, Olivier |
title |
On Recognizable Languages of Infinite Pictures |
title_short |
On Recognizable Languages of Infinite Pictures |
title_full |
On Recognizable Languages of Infinite Pictures |
title_fullStr |
On Recognizable Languages of Infinite Pictures |
title_full_unstemmed |
On Recognizable Languages of Infinite Pictures |
title_sort |
on recognizable languages of infinite pictures |
publishDate |
2009 |
url |
http://arxiv.org/abs/0901.3828 |
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sami |
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sami |
op_source |
arXiv |
op_relation |
International Journal of Foundations of Computer Science 15, 6 (2004) 823-840 10670/1.ve2m4b http://arxiv.org/abs/0901.3828 |
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