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Regular Languages of Words over Countable Linear Orderings

  • Olivier Carton
  • Thomas Colcombet
  • Gabriele Puppis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)

Abstract

We develop an algebraic model for recognizing languages of words indexed by countable linear orderings. This notion of recognizability is effectively equivalent to definability in monadic second-order (MSO) logic. The proofs also imply the first known collapse result for MSO logic over countable linear orderings.

Keywords

Convex Subset Evaluation Tree Linear Ordering Expressive Power Regular Language 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bedon, N., Bès, A., Carton, O., Rispal, C.: Logic and rational languages of words indexed by linear orderings. Theoretical Computer Science 46(4), 737–760 (2010)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Bruyère, V., Carton, O.: Automata on linear orderings. Journal of Computer and System Sciences 73(1), 1–24 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Büchi, J.R.: Transfinite automata recursions and weak second order theory of ordinals. In: Proc. Int. Congress Logic, Methodology, and Philosophy of Science, Jerusalem, pp. 2–23. North Holland, Amsterdam (1964)Google Scholar
  4. 4.
    Büchi, J.R.: On a decision method in restricted second order arithmetic. In: Proceedings of the International Congress for Logic, Methodology and Philosophy of Science, pp. 1–11. Stanford University Press, Stanford (1962)Google Scholar
  5. 5.
    Colcombet, T.: Factorisation forests for infinite words and applications to countable scattered linear orderings. Theoretical Computer Science 411, 751–764 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Feferman, S., Vaught, R.: The first-order properties of products of algebraic systems. Fundamenta Mathematicae 47, 57–103 (1959)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Kechris, A.S.: Classical Descriptive Set Theory. Graduate Texts in Mathematics. Springer, Heidelberg (1995)CrossRefzbMATHGoogle Scholar
  8. 8.
    Rabin, M.O.: Decidability of second-order theories and automata on infinite trees. Transactions of the American Mathematical Society 141, 1–35 (1969)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Ramsey, F.P.: On a problem of formal logic. Proceedings of the London Mathematical Society 30, 264–286 (1929)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Rispal, C., Carton, O.: Complementation of rational sets on countable scattered linear orderings. International Journal of Foundations of Computer Science 16(4), 767–786 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Rosenstein, J.G.: Linear Orderings. Academic Press, London (1982)zbMATHGoogle Scholar
  12. 12.
    Shelah, S.: The monadic theory of order. Annals of Mathematics 102, 379–419 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Thomas, W.: Languages, automata, and logic. In: Handbook of Formal Languages, vol. 3, pp. 389–455. Springer, Heidelberg (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Olivier Carton
    • 1
  • Thomas Colcombet
    • 2
  • Gabriele Puppis
    • 3
  1. 1.University Paris Diderot, LIAFAFrance
  2. 2.CNRS/LIAFAFrance
  3. 3.Department of Computer ScienceOxford UniversityUK

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