Skip to main content
SpringerLink
Log in

Invariants of Automatic Presentations and Semi-synchronous Transductions

  • Conference paper
STACS 2006 (STACS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3884))

Included in the following conference series:

Abstract

Automatic structures are countable structures finitely presentable by a collection of automata. We study questions related to properties invariant with respect to the choice of an automatic presentation. We give a negative answer to a question of Rubin concerning definability of intrinsically regular relations by showing that order-invariant first-order logic can be stronger than first-order logic with counting on automatic structures. We introduce a notion of equivalence of automatic presentations, define semi-synchronous transductions, and show how these concepts correspond. Our main result is that a one-to-one function on words preserves regularity as well as non-regularity of all relations iff it is a semi-synchronous transduction. We also characterize automatic presentations of the complete structures of Blumensath and Grädel.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allouche, J.-P., Shallit, J.: Automatic Sequences, Theory, Applications, Generalizations. Cambridge University Press, Cambridge (2003)

    Book  MATH  Google Scholar 

  2. Berstel, J.: Transductions and Context-Free Languages. Teubner, Stuttgart (1979)

    Google Scholar 

  3. Bès, A.: Undecidable extensions of Büchi arithmetic and Cobham-Semënov theorem. J. Symb. Log. 62(4), 1280–1296 (1997)

    Article  MATH  Google Scholar 

  4. Blumensath, A.: Automatic structures. Diploma thesis, RWTH-Aachen (1999)

    Google Scholar 

  5. Blumensath, A., Grädel, E.: Automatic Structures. In: Proceedings of 15th IEEE Symposium on Logic in Computer Science LICS 2000, pp. 51–62 (2000)

    Google Scholar 

  6. Blumensath, A., Grädel, E.: Finite presentations of infinite structures: Automata and interpretations. Theory of Computing Systems 37, 641–674 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bruyère, V., Hansel, G., Michaux, C., Villemaire, R.: Logic and p-recognizable sets of integers. Bull. Belg. Math. Soc. 1, 191–238 (1994)

    MathSciNet  MATH  Google Scholar 

  8. Cannon, J.W., Epstein, D.B.A., Holt, D.F., Levy, S.V.F., Paterson, M.S., Thurston, W.P.: Word processing in groups. Jones and Barlett Publ., Boston (1992)

    MATH  Google Scholar 

  9. Elgot, C.C., Mezei, J.E.: On relations defined by generalized finite automata. IBM J. Research and Development 9, 47–68 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  10. Frougny, C., Sakarovitch, J.: Synchronized rational relations of finite and infinite words. Theor. Comput. Sci. 108, 45–82 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hella, L.: Definability hierarchies of generalized quantifiers. Ann. Pure Appl. Logic 43, 235–271 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hodgson, B.R.: On direct products of automaton decidable theories. TCS 19, 331–335 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  13. Khoussainov, B., Nerode, A.: Automatic presentations of structures. In: Leivant, D. (ed.) LCC 1994. LNCS, vol. 960, pp. 367–392. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  14. Khoussainov, B., Nies, A., Rubin, S., Stephan, F.: Automatic structures: Richness and limitations. In: LICS, pp. 44–53. IEEE Computer Society, Los Alamitos (2004)

    Google Scholar 

  15. Khoussainov, B., Rubin, S.: Automatic structures: Overview and future directions. Journal of Automata, Languages and Combinatorics 8(2), 287–301 (2003)

    MathSciNet  MATH  Google Scholar 

  16. Khoussainov, B., Rubin, S., Stephan, F.: Definability and regularity in automatic structures. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 440–451. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  17. Kuske, D.: Is cantor’s theorem automatic? In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 332–345. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  18. Libkin, L.: Elements of Finite Model Theory. Texts in Theoretical Computer Science. Springer, Heidelberg (2004)

    Book  MATH  Google Scholar 

  19. Otto, M.: Epsilon-logic is more expressive than first-order logic over finite structures. J. Symb. Logic 65, 1749–1757 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  20. Rubin, S.: Automatic structures. Ph.D. thesis, University of Auckland, NZ (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematische Grundlagen der Informatik, RWTH Aachen, Germany

    Vince Bárány

Authors
  1. Vince Bárány
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. LIF, CNRS & Univ. de Provence,, Marseille, France

    Bruno Durand

  2. RWTH Aachen University,, Lehrstuhl Informatik 7,, 52056,, Aachen,, Germany

    Wolfgang Thomas

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bárány, V. (2006). Invariants of Automatic Presentations and Semi-synchronous Transductions. In: Durand, B., Thomas, W. (eds) STACS 2006. STACS 2006. Lecture Notes in Computer Science, vol 3884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11672142_23

Download citation

  • DOI: https://doi.org/10.1007/11672142_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32301-3

  • Online ISBN: 978-3-540-32288-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation