Two-way automata and regular languages of overlapping tiles

Anne Dicky (1, 2) , David Janin (2, 1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 PoSET - Models for a Structured Programming of Space and Time

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.

Mots clés: languages of words; languages of overlapping tiles; two-way automata; pebble automata; free inverse monoids

Domaines: Théorie et langage formel [cs.FL]; Logique [math.LO]

Anne Dicky, David Janin. Two-way automata and regular languages of overlapping tiles. Fundamenta Informaticae, 2015, 142, pp.1-33. ⟨10.3233/FI-2015-1280⟩. ⟨hal-00717572v3⟩