Tiling Systems over Infinite Pictures and Their Acceptance Conditions

Languages of infinite two-dimensional words (ω-pictures) are studied in the automata theoretic setting of tiling systems. We show that a hierarchy of acceptance conditions as known from the theory of ω-languages can be established also over pictures. Since the usual pumping arguments fail, new proof techniques are necessary. Finally, we show that (unlike the case of ω-languages) none of the considered acceptance conditions leads to a class of infinitary picture languages which is closed under complementation.