Languages of Profinite Words and the Limitedness Problem

  • Szymon Toruńczyk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7392)


We present a new framework for the limitedness problem. The key novelty is a description using profinite words, which unifies and simplifies the previous approaches, allowing a seamless extension of the theory of regular languages. We also define a logic over profinite words, called MSO+inf and show that the satisfiability problem of MSO+\(\mathbb B\) reduces to the satisfiability problem of our logic.


Regular Expression Convergent Sequence Regular Language Limitedness Problem Topological Semigroup 
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  1. 1.
    Abdulla, P.A., Krcal, P., Yi, W.: R-Automata. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 67–81. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Bojańczyk, M.: A Bounding Quantifier. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 41–55. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Bojańczyk, M.: Beyond ω-regular languages. In: STACS, pp. 11–16 (2010)Google Scholar
  4. 4.
    Bojańczyk, M., Colcombet, T.: Bounds in ω-regularity. In: Logic in Computer Science, pp. 285–296 (2006)Google Scholar
  5. 5.
    Colcombet, T.: The Theory of Stabilisation Monoids and Regular Cost Functions. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part II. LNCS, vol. 5556, pp. 139–150. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Colcombet, T.: Regular cost functions, Part I: Logic and algebra over words (2011) (submitted)Google Scholar
  7. 7.
    Hashiguchi, K.: Limitedness theorem on finite automata with distance functions. Journal of Computer and System Sciences 24, 233–244 (1982)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Kirsten, D.: Distance desert automata and the star height problem. Theoretical Informatics and Applications 39(3), 455–511 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Krob, D.: The Equality Problem for Rational Series with Multiplicities in the Tropical Semiring is Undecidable. In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 101–112. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  10. 10.
    Leung, H.: On the topological structure of a finitely generated semigroup of matrices. Semigroup Forum 37, 273–278 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Pin, J.-É.: Profinite methods in automata theory. In: Albers, S., Marion, J.-Y. (eds.) STACS. LIPIcs, vol. 3, pp. 31–50. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany (2009)Google Scholar
  12. 12.
    Simon, I.: On semigroups of matrices over the tropical semiring. ITA 28(3-4), 277–294 (1994)zbMATHGoogle Scholar
  13. 13.
    Skrzypczak, M.: Separation property for ωB- and ωS-regular languages (submitted, 2012)Google Scholar
  14. 14.
    Toruńczyk, S.: Languages of profinite words and the limitedness problem (2012),

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Szymon Toruńczyk
    • 1
  1. 1.University of WarsawPoland

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