Skip to main content

Boolean Algebras of Regular Languages

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6795))

Abstract

We characterize up to isomorphism the Boolean algebras of regular languages and of regular aperiodic languages, and show decidability of classes of regular languages related to these characterizations.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Choffrut, C., Karhumäki, J.: Combinatorics of Words. In: Handbook of Formal Languages. Springer, Berlin (1997)

    Google Scholar 

  2. Ershov, Y.L.: Relatively complemented distributive lattices. Algebra and Logic 18(6), 680–722 (1979) (Russian, there is an English translation)

    Google Scholar 

  3. Gehrke, M., Grigorieff, S., Pin, J.-É.: Duality and equational theory of regular languages. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 246–257. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  4. Goncharov, S.S.: Countable Boolean Algebras and Decidability. Plenum, New York (1996)

    MATH  Google Scholar 

  5. Hanf, W.: The boolean algebra of logic. Bull. Amer. Math. Soc. 20(4), 456–502 (1975)

    Google Scholar 

  6. Ketonen, J.: The structure of countable Boolean algebras. Annals of Mathematics 108, 41–89 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lempp, S., Peretyat’kin, M., Solomon, R.: The Lindenbaum algebra of the theory of the class of all finite models. Journal of Mathematical Logic 2(2), 145–225 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Pin, J.-E.: Unpublished manuscript on regular languages

    Google Scholar 

  9. Pippenger, N.: Regular languages and Stone duality. Theory of Computing Systems 30(2), 121–134 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  10. Perrin, D., Pin, J.-E.: Infinite Words. Pure and Applied Mathematics, vol. 141. Elsevier, Amsterdam (2004)

    MATH  Google Scholar 

  11. Selivanov, V.L.: Universal Boolean algebras with applications. In: Abstracts of Int. Conf. in Algebra, Novosibirsk, p. 127 (1991) (in Russian)

    Google Scholar 

  12. Selivanov, V.L.: Hierarchies, Numerations, Index Sets. Handwritten Notes, 290 pp (1992)

    Google Scholar 

  13. Selivanov, V.L.: Positive structures. In: Barry Cooper, S., Goncharov, S.S. (eds.) Computability and Models, Perspectives East and West, pp. 321–350. Kluwer Academic/Plenum Publishers, New York (2003)

    Google Scholar 

  14. Sikorski, R.: Boolean Algebras. Springer, Berlin (1964)

    MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  16. Szilard, A., Yu, S., Zhang, K., Shallit, J.: Characterizing Regular Languages with Polynomial Densities. In: Havel, I.M., Koubek, V. (eds.) MFCS 1992. LNCS, vol. 629, Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  17. Thomas, W.: Languages, automata and logic. In: Handbook of Formal Language Theory, vol. B, pp. 133–191 (1996)

    Google Scholar 

  18. Yu, S.: Regular Languages. In: Rozenberg, G., Salomaa, A. (eds.) A chapter of Handbook of Formal Languages. Springer, Heidelberg (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Selivanov, V., Konovalov, A. (2011). Boolean Algebras of Regular Languages. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22321-1_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22320-4

  • Online ISBN: 978-3-642-22321-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics