Two-way automata and regular languages of overlapping tiles

Anne Dicky 1, 2 David Janin 2, 1
2 PoSET - Models for a Structured Programming of Space and Time
LaBRI - Laboratoire Bordelais de Recherche en Informatique, SCRIME - Studio de Création et de Recherche en Informatique et Musique Électroacoustique, Inria Bordeaux - Sud-Ouest
Abstract : We consider classes of languages of overlapping tiles, i.e., subsets of the McAlister monoid: the class REG of languages definable by Kleene’s regular expressions, the class MSO of languages definable by formulas of monadic second-order logic, and the class REC of languages definable by morphisms into finite monoids. By extending the semantics of finite-state two-way au- tomata (possibly with pebbles) from languages of words to languages of tiles, we obtain a complete characterization of the classes REG and MSO. In particular, we show that adding pebbles strictly increases the expressive power of two-way automata recognizing languages of tiles, but the hierarchy induced by the number of allowed pebbles collapses to level one.
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Anne Dicky, David Janin. Two-way automata and regular languages of overlapping tiles. Fundamenta Informaticae, Polskie Towarzystwo Matematyczne, 2015, 142, pp.1-33. ⟨10.3233/FI-2015-1280⟩. ⟨hal-00717572v3⟩

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