关于无限图像的可识别语言
On Recognizable Languages of Infinite Pictures
摘要：
在最近的一篇论文中，Altenbernd，Thomas和Wöhrle考虑了有限镶嵌系统对无限二维词（无限图像）语言的接受，通常的接受条件，如Büchi和Muller的，首先用于无限词。作者要求使用自动机模型对长度为$ω^2$的序数词逐行比较平铺系统接受度和图片接受度。本文给出了这个问题的一个解决方案，证明了读长度为$ω^2$的字的Büchi或Choueka自动机逐行接受的所有无限图像的语言都是由有限平铺系统识别的Büchi，但反之则不成立。我们也给出了另外两个问题的答案，这是由Altenbernd，托马斯和Wöhrle提出的，表明它是不可判定的是否Büchi可识别的语言的无限图片是E-可识别的（分别，A-可识别的）。
英文摘要：
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).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
