On recognizable languages of infinite pictures

In a recent paper, Altenbernd, Thomas and Wohrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the Buchi 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 Buchi or Choueka automata reading words of length omega(2) are Buchi 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 Wohrle, showing that it is undecidable whether a Buchi recognizable language of infinite pictures is F-recognizable (respectively, A-recognizable).