On the Use of Guards for Logics with Data

Thomas Colcombet (1) , Clemens Ley (2) , Gabriele Puppis (3)

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

The notion of orbit finite data monoid was recently introduced by Bojanczyk as an algebraic object for defining recognizable languages of data words. Following Buchi's approach, we introduce the new logic 'rigidly guarded MSO' and show that the data languages definable in this logic are exactly those recognizable by orbit finite data monoids. We also establish, following this time the approach of Schutzenberger, McNaughton and Papert, that the first-order variant of this logic defines exactly the languages recognizable by aperiodic orbit finite data monoids. Finally, we give a variant of the logic that captures the larger class of languages recognized by non-deterministic finite memory automata.

Domaines: Logique en informatique [cs.LO]

Thomas Colcombet, Clemens Ley, Gabriele Puppis. On the Use of Guards for Logics with Data. Proceedings of MFCS 2011, 2011, Warsaw, Poland. pp.243-255, ⟨10.1007/978-3-642-22993-0_24⟩. ⟨hal-00717748⟩