Logics with Rigidly Guarded Data Tests

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

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
2 Department of Computer Science [Oxford]
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 a variant of monadic second-order logic with data equality tests that captures precisely the data languages recognizable by orbit finite data monoids. We also establish, following this time the approach of Schutzenberger, McNaughton and Papert, that the first-order fragment of this logic defines exactly the data languages recognizable by aperiodic orbit finite data monoids. Finally, we consider another variant of the logic that can be interpreted over generic structures with data. The data languages defined in this variant are also recognized by unambiguous finite memory automata.

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

Thomas Colcombet, Clemens Ley, Gabriele Puppis. Logics with Rigidly Guarded Data Tests. Proceedings of FREC 2014 - Frontiers of Recognizability, Apr 2014, Marseille, France. ⟨10.2168/LMCS-11(3:10)2015⟩. ⟨hal-01219499⟩