Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Bojańczyk, M.: A Bounding Quantifier. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 41–55. Springer, Heidelberg (2004)
Bojańczyk, M.: Beyond ω-regular languages. In: STACS, pp. 11–16 (2010)
Bojańczyk, M., Colcombet, T.: Bounds in ω-regularity. In: Logic in Computer Science, pp. 285–296 (2006)
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)
Colcombet, T.: Regular cost functions, Part I: Logic and algebra over words (2011) (submitted)
Hashiguchi, K.: Limitedness theorem on finite automata with distance functions. Journal of Computer and System Sciences 24, 233–244 (1982)
Kirsten, D.: Distance desert automata and the star height problem. Theoretical Informatics and Applications 39(3), 455–511 (2005)
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)
Leung, H.: On the topological structure of a finitely generated semigroup of matrices. Semigroup Forum 37, 273–278 (1988)
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)
Simon, I.: On semigroups of matrices over the tropical semiring. ITA 28(3-4), 277–294 (1994)
Skrzypczak, M.: Separation property for ωB- and ωS-regular languages (submitted, 2012)
Toruńczyk, S.: Languages of profinite words and the limitedness problem (2012), http://www.mimuw.edu.pl/~szymtor/papers/BS-icalp.pdf
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Toruńczyk, S. (2012). Languages of Profinite Words and the Limitedness Problem. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_35
Download citation
DOI: https://doi.org/10.1007/978-3-642-31585-5_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31584-8
Online ISBN: 978-3-642-31585-5
eBook Packages: Computer ScienceComputer Science (R0)