Abstract : 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.
https://hal-upec-upem.archives-ouvertes.fr/hal-00733458
Contributor : Arnaud Carayol <>
Submitted on : Tuesday, July 4, 2017 - 5:59:43 PM Last modification on : Wednesday, February 26, 2020 - 7:06:07 PM Long-term archiving on: : Friday, December 15, 2017 - 2:39:52 AM
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⟩