Skip to main content
SpringerLink
Log in

\({\mathcal C}\)-Varieties, Actions and Wreath Product

  • Conference paper
Book cover LATIN 2006: Theoretical Informatics (LATIN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3887))

Included in the following conference series:

  • 987 Accesses

Abstract

Motivated by open problems in language theory, logic and circuit complexity, Straubing generalized Eilenberg’s variety theory, introducing the \({\mathcal C}\)-varieties. As a further contribution to this theory, this paper first studies a new \({\mathcal C}\)-variety of languages, lying somewhere between star-free and regular languages. Then, continuing the early works of Esik-Ito, we extend the wreath product to \({\mathcal C}\)-varieties and generalize the wreath product principle, a powerful tool originally designed by Straubing for varieties. We use it to derive a characterization of the operations L→ LaA* and L → La on languages. Finally, we investigate the decidability of the operation V →V ∗ LI (the wreath product by locally trivial semigroups) and solve it explicitely in several non-trivial cases.

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. Brzozowski, J.A., Simon, I.: Characterizations of locally testable events. Discrete Math. 4, 243–271 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  2. Eilenberg, S.: Automata, languages, and machines, vol. B. Academic Press, London (1976)

    MATH  Google Scholar 

  3. Ésik, Z.: Extended temporal logic on finite words and wreath products of monoids with distinguished generators. In: Ito, M., Toyama, M. (eds.) DLT 2002. LNCS, vol. 2450, pp. 43–58. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Ésik, Z., Ito, M.: Temporal logic with cyclic counting and the degree of aperiodicity of finite automata. Acta Cybernetica 16, 1–28 (2003)

    MathSciNet  MATH  Google Scholar 

  5. Ésik, Z., Larsen, K.G.: Regular languages defined by Lindström quantifiers. Theoret. Informatics Appl. 37, 179–242 (2003)

    Article  MATH  Google Scholar 

  6. Hanf, W.: Model-theoretic methods in the study of elementary logic. In: Theory of Models, pp. 132–145. North-Holland, Amsterdam (1965)

    Google Scholar 

  7. Kunc, M.: Equational description of pseudovarieties of homomorphisms. Theoret. Informatics Appl. 37, 243–254 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Peled, D., Wilke, T.: Stutter-invariant temporal properties are expressible without the next-time operator. Inf. Process. Lett. 63(5), 243–246 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pin, J.-É.: Varieties of formal languages. North Oxford, London (1986)

    Book  MATH  Google Scholar 

  10. Pin, J.-É.: Syntactic semigroups. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of formal languages, ch. 10, vol. 1. Springer, Heidelberg (1997)

    Google Scholar 

  11. Pin, J.-É., Straubing, H.: Some results on C-varieties. Theoret. Informatics Appl. 39, 239–262 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Pin, J.-É., Weil, P.: The wreath product principle for ordered semigroups. Communications in Algebra 30, 5677–5713 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Reiterman, J.: The Birkhoff theorem for finite algebras. Alg. Univ. 14(1), 1–10 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  14. Straubing, H.: Families of recognizable sets corresponding to certain varieties of finite monoids. J. Pure Appl. Algebra 15(3), 305–318 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  15. Straubing, H.: Finite semigroup varieties of the form V*D. J. Pure Appl. Algebra 36(1), 53–94 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  16. Straubing, H.: Finite automata, formal logic, and circuit complexity. Birkhäuser Boston Inc., Basel (1994)

    Book  MATH  Google Scholar 

  17. Straubing, H.: On logical descriptions of regular languages. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 528–538. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  18. Thérien, D., Weiss, A.: Graph congruences and wreath products. J. Pure Appl. Algebra 36 (1985)

    Google Scholar 

  19. Tilson, B.: Categories as algebra: an essential ingredient in the theory of monoids. J. Pure Appl. Algebra 48(1-2), 83–198 (1987)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIAFA, Université Paris VII and CNRS, Case 7014, 2 Place Jussieu, 75251 Cedex 05, Paris, France

    Laura Chaubard

Authors
  1. Laura Chaubard
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Business, Universidad Adolfo Ibáñez, Chile

    José R. Correa

  2. Dept. of Computer Science, University of Chile, Blanco Encalada 2120, 3er piso, Santiago, Chile

    Alejandro Hevia

  3. Dept. Ing. Matemática & Ctr. de Modelamiento Matemático, UMI 2807 U. Chile–CNRS, Chile

    Marcos Kiwi

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chaubard, L. (2006). \({\mathcal C}\)-Varieties, Actions and Wreath Product. In: Correa, J.R., Hevia, A., Kiwi, M. (eds) LATIN 2006: Theoretical Informatics. LATIN 2006. Lecture Notes in Computer Science, vol 3887. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11682462_28

Download citation

  • DOI: https://doi.org/10.1007/11682462_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32755-4

  • Online ISBN: 978-3-540-32756-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation