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Article type: Research Article
Authors: Dicky, Annea | Janin, Davida; *
Affiliations: [a] Université de Bordeaux, LaBRI UMR 5800, 351, cours de la Libération, F-33405 Talence, France. dicky@labri.fr, janin@labri.fr
Correspondence: [*] Address for correspondence: Université de Bordeaux, LaBRI UMR 5800, 351, cours de la Libération, F-33405 Talence, France.
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 automata (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.
Keywords: two-way automata, word languages, overlapping tile languages, regular languages, McAlister inverse monoid
DOI: 10.3233/FI-2015-1278
Journal: Fundamenta Informaticae, vol. 141, no. 4, pp. 311-343, 2015
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