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.
Arnaud Carayol has been supported by the project AMIS (ANR 2010 JCJC 0203 01 AMIS). Both authors received partial support from the project TÁMOP-4.2.1/B-09/1/KONV-2010-0005 “Creating the Center of Excellence at the University of Szeged”, supported by the European Union and co-financed by the European Regional Fund. Zoltán Ésik was also partly supported by the National Foundation of Hungary for Scientific Research, grant no. K 75249, and by a chair Labex Bézout as part of the program “Investissements d’Avenir” (ANR-10-LABX-58).
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Carayol, A., Ésik, Z. (2012). A Context-Free Linear Ordering with an Undecidable First-Order Theory. In: Baeten, J.C.M., Ball, T., de Boer, F.S. (eds) Theoretical Computer Science. TCS 2012. Lecture Notes in Computer Science, vol 7604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33475-7_8
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