Regular Languages of Words over Countable Linear Orderings

Gabriele Puppis (1) , Thomas Colcombet (2) , Olivier Carton (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We develop an algebraic model for recognizing languages of words indexed by countable linear orderings. This notion of recognizability is effectively equivalent to definability in monadic second-order (MSO) logic. The proofs also imply the first known collapse result for MSO logic over countable linear orderings.

Domaines: Théorie et langage formel [cs.FL]

Gabriele Puppis, Thomas Colcombet, Olivier Carton. Regular Languages of Words over Countable Linear Orderings. Proceedings of ICALP 2011, 2011, Zurich, Switzerland. pp.125-136, ⟨10.1007/978-3-642-22012-8_9⟩. ⟨hal-00717752⟩