A context-free linear ordering with an undecidable first-order theory

Arnaud Carayol (1) , Zoltan Esik (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 Institute of Informatics

The words of a context-free language, ordered by the lexicographic ordering, form a context-free linear ordering. It is well-known that the linear orderings associated with deterministic context-free languages have a decidable monadic second-order theory. In stark contrast, we give an example of a context-free language whose lexicographic ordering has an undecidable first-order theory.

Domaines: Informatique [cs]; Logique en informatique [cs.LO]

Arnaud Carayol, Zoltan Esik. A context-free linear ordering with an undecidable first-order theory. 7th International Conference on Theoretical Computer Science (TCS), Sep 2012, Amsterdam, Netherlands. pp.104-118, ⟨10.1007/978-3-642-33475-7_8⟩. ⟨hal-00733458⟩