On Recognizable Languages of Infinite Pictures

Olivier Finkel (1)

1 ELM - Équipe de Logique Mathématique

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 $\omega^2$. We give in this paper a solution to this problem, showing that all languages of infinite pictures which are accepted row by row by Büchi or Choueka automata reading words of length $\omega^2$ 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).

Mots clés: Languages of infinite pictures; tiling systems; ordinal Büchi automaton; topological complexity; Borel and analytic sets; E-recognizable; A-recognizable; decision problems.; decision problems

Domaines: Logique en informatique [cs.LO]; Complexité [cs.CC]; Logique [math.LO]

Olivier Finkel. On Recognizable Languages of Infinite Pictures. International Journal of Foundations of Computer Science, 2004, 15 (6), pp.823-840. ⟨hal-00355793⟩