Tiling systems over infinite pictures and their acceptance conditions

Authors:
Jan-Henrik Altenbernd;Wolfgang Thomas;Stefan Wöhrle
Affiliations:
Lehrstuhl für Informatik VII, RWTH Aachen, Aachen, Germany;Lehrstuhl für Informatik VII, RWTH Aachen, Aachen, Germany;Lehrstuhl für Informatik VII, RWTH Aachen, Aachen, Germany
Venue:
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Year:
2002

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Abstract

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.