Skip to main content
SpringerLink
Log in

Geometrical Closure of Binary \(V_{3/2}\) Languages

  • Conference paper
  • First Online:
Language and Automata Theory and Applications (LATA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11417))

Abstract

We define the geometrical closure of a language over a \(j\)-ary alphabet, and we prove that in the case of dimension 2 the family \(V_{3/2}\) in the Straubing-Thérien hierarchy of languages is closed under this operation. In other words, the geometrical closure of a \(V_{3/2}\) binary language is still a \(V_{3/2}\) language. This is achieved by carrying out some transformations over a regular expression representing the \(V_{3/2}\) language, which leads to a \(V_{3/2}\) regular expression for the geometrical closure.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and 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

Institutional subscriptions

References

  1. Arfi, M.: Opérations polynomiales et hiérarchies de concaténation. Theoret. Comput. Sci. 91(1), 71–84 (1991)

    Article  MathSciNet  Google Scholar 

  2. Baruah, S.K., Rosier, L.E., Howell, R.R.: Algorithms and complexity concerning the preemptive scheduling of periodic, real-time tasks on one processor. Real-Time Syst. 2(4), 301–324 (1990)

    Article  Google Scholar 

  3. Béal, M.-P., Champarnaud, J.-M., Dubernard, J.-P., Jeanne, H., Lombardy, S.: Decidability of geometricity of regular languages. In: Yen, H.-C., Ibarra, O.H. (eds.) DLT 2012. LNCS, vol. 7410, pp. 62–72. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31653-1_7

    Chapter  Google Scholar 

  4. Blanpain, B., Champarnaud, J.M., Dubernard, J.P.: Geometrical languages. In: LATA, Report 35/07, pp. 127–138. Research Group on Mathematical Linguistics, Universitat Rovira i Virgili, Tarragona (2007)

    Google Scholar 

  5. Bouajjani, A., Muscholl, A., Touili, T.: Permutation rewriting and algorithmic verification. Inf. Comput. 205(2), 199–224 (2007)

    Article  MathSciNet  Google Scholar 

  6. Champarnaud, J.-M., Dubernard, J.-P., Jeanne, H.: Geometricity of binary regular languages. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 178–189. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13089-2_15

    Chapter  Google Scholar 

  7. Geniet, D., Largeteau, G.: WCET free time analysis of hard real-time systems on multiprocessors: a regular language-based model. Theoret. Comput. Sci. 388(1–3), 26–52 (2007)

    Article  MathSciNet  Google Scholar 

  8. Guaiana, G., Restivo, A., Salemi, S.: On the trace product and some families of languages closed under partial commutations. J. Automata Lang. Comb. 9(1), 61–79 (2004)

    MathSciNet  MATH  Google Scholar 

  9. Largeteau, G., Geniet, D., Andrès, É.: Discrete geometry applied in hard real-time systems validation. In: Andres, E., Damiand, G., Lienhardt, P. (eds.) DGCI 2005. LNCS, vol. 3429, pp. 23–33. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31965-8_3

    Chapter  MATH  Google Scholar 

  10. Mignot, L.: Application: geometrical closure of \(V_{3/2}\) binary expressions. http://ludovicmignot.free.fr/programmes/geomClosure/index.html. Accessed 27 Oct 2018

  11. Pin, J.É.: The dot-depth hierarchy, 45 years later. In: The Role of Theory in Computer Science, pp. 177–202. World Scientific (2017)

    Google Scholar 

  12. Pin, J.É., Weil, P.: Ponynominal closure and unambiguous product. Theory Comput. Syst. 30(4), 383–422 (1997)

    Article  MathSciNet  Google Scholar 

  13. Place, T., Zeitoun, M.: Concatenation hierarchies: new bottle, old wine. In: Weil, P. (ed.) CSR 2017. LNCS, vol. 10304, pp. 25–37. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-58747-9_5

    Chapter  Google Scholar 

  14. Place, T., Zeitoun, M.: Generic results for concatenation hierarchies. Theory Comput. Syst. 1–53 (2017). https://doi.org/10.1007/s00224-018-9867-0

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

    Article  MathSciNet  Google Scholar 

  16. Thérien, D.: Classification of finite monoids: the language approach. Theoret. Comput. Sci. 14, 195–208 (1981)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LITIS EA 4108, Université de Rouen Normandie, Avenue de l’Université, 76801, Saint-Étienne-du-Rouvray, France

    Jean-Philippe Dubernard & Giovanna Guaiana

  2. GR²IF, Université de Rouen Normandie, Avenue de l’Université, 76801, Saint-Étienne-du-Rouvray, France

    Ludovic Mignot

Authors
  1. Jean-Philippe Dubernard
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giovanna Guaiana
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ludovic Mignot
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ludovic Mignot .

Editor information

Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  2. Saint Petersburg State University, St. Petersburg, Russia

    Alexander Okhotin

  3. Ariel University, Ariel, Israel

    Dana Shapira

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dubernard, JP., Guaiana, G., Mignot, L. (2019). Geometrical Closure of Binary \(V_{3/2}\) Languages. In: Martín-Vide, C., Okhotin, A., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2019. Lecture Notes in Computer Science(), vol 11417. Springer, Cham. https://doi.org/10.1007/978-3-030-13435-8_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-13435-8_22

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-13434-1

  • Online ISBN: 978-3-030-13435-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation