Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

String Attractors of Fixed Points of k-Bonacci-Like Morphisms

  • Conference paper
  • First Online:
Combinatorics on Words (WORDS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13899))

Included in the following conference series:

  • 319 Accesses

Abstract

Firstly studied by Kempa and Prezza in 2018 as the cement of text compression algorithms, string attractors have become a compelling object of theoretical research within the community of combinatorics on words. In this context, they have been studied for several families of finite and infinite words. In this paper, we obtain string attractors of prefixes of particular infinite words generalizing k-bonacci words (including the famous Fibonacci word) and obtained as fixed points of k-bonacci-like morphisms. In fact, our description involves the numeration systems classically derived from the considered morphisms.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 64.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 84.99
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. Allouche, J.P., Shallit, J.: Automatic sequences, theory, applications, generalizations Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546563

  2. Berthé, V., Rigo, M. (eds.): Combinatorics, automata and number theory, Encyclopedia of Mathematics and its Applications, vol. 135. Cambridge University Press, Cambridge (2010). https://doi.org/10.1017/CBO9780511777653

  3. Bertrand-Mathis, A.: Comment écrire les nombres entiers dans une base qui n’est pas entière. Acta Math. Hungar. 54(3–4), 237–241 (1989). https://doi.org/10.1007/BF01952053

    Article  MathSciNet  MATH  Google Scholar 

  4. Bonizzoni, P., De Felice, C., Zaccagnino, R., Zizza, R.: Inverse Lyndon words and inverse Lyndon factorizations of words. Adv. in Appl. Math. 101, 281–319 (2018). https://doi.org/10.1016/j.aam.2018.08.005

    Article  MathSciNet  MATH  Google Scholar 

  5. Charlier, E., Cisternino, C., Stipulanti, M.: A full characterization of Bertrand numeration systems. In: Developments in Language Theory, vol. 13257. LNCS, pp. 102–114. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-05578-2_8

  6. Charlier, E., Philibert, M., Stipulanti, M.: Nyldon words. J. Combin. Theory Ser. A 167, 60–90 (2019). https://doi.org/10.1016/j.jcta.2019.04.002

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen, K.T., Fox, R.H., Lyndon, R.C.: Free differential calculus. IV. The quotient groups of the lower central series. Ann. of Math. 2(68), 81–95 (1958). https://doi.org/10.2307/1970044

  8. Christiansen, A.R., Ettienne, M.B., Kociumaka, T., Navarro, G., Prezza, N.: Optimal-time dictionary-compressed indexes. ACM Trans. Algorithms 17(1), 8:1–8:39 (2021). https://doi.org/10.1145/3426473

  9. Dumont, J.M., Thomas, A.: Systèmes de numération et fonctions fractales relatifs aux substitutions. Theoret. Comput. Sci. 65(2), 153–169 (1989). https://doi.org/10.1016/0304-3975(89)90041-8

    Article  MathSciNet  MATH  Google Scholar 

  10. Duval, J.P.: Mots de Lyndon et périodicité. RAIRO Inform. Théor. 14(2), 181–191 (1980). https://doi.org/10.1051/ita/1980140201811

    Article  MathSciNet  MATH  Google Scholar 

  11. Dvořáková, L.: String attractors of episturmian sequence, preprint available at arXiv:2211.01660 (2022)

  12. Fabre, S.: Substitutions et \(\beta \)-systèmes de numération. Theoret. Comput. Sci. 137(2), 219–236 (1995). https://doi.org/10.1016/0304-3975(95)91132-A

    Article  MathSciNet  MATH  Google Scholar 

  13. Frougny, C.: On the sequentiality of the successor function. Inform. Comput. 139(1), 17–38 (1997). https://doi.org/10.1006/inco.1997.2650

    Article  MathSciNet  MATH  Google Scholar 

  14. Gewurz, D.A., Merola, F.: Numeration and enumeration. European J. Combin. 33(7), 1547–1556 (2012). https://doi.org/10.1016/j.ejc.2012.03.017

    Article  MathSciNet  MATH  Google Scholar 

  15. Gheeraert, F., Restivo, A., Romana, G., Sciortino, M., Stipulanti, M.: New string attractor-based complexities on infinite words (2023), work in progress

    Google Scholar 

  16. Gheeraert, F., Romana, G., Stipulanti, M.: String attractors of fixed points of \(k\)-bonacci-like morphisms, long version available at arXiv:2302.13647 (2023)

  17. Hollander, M.: Greedy numeration systems and regularity. Theory Comput. Syst. 31(2), 111–133 (1998). https://doi.org/10.1007/s002240000082

    Article  MathSciNet  MATH  Google Scholar 

  18. Kempa, D., Prezza, N.: At the roots of dictionary compression: string attractors. In: STOC 2018–Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, pp. 827–840. ACM, New York (2018). https://doi.org/10.1145/3188745.3188814

  19. Kutsukake, K., Matsumoto, T., Nakashima, Y., Inenaga, S., Bannai, H., Takeda, M.: On repetitiveness measures of Thue-Morse words. In: Boucher, C., Thankachan, S.V. (eds.) SPIRE 2020. vol. 12303. LNCS, pp. 213–220. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59212-7_15

  20. Lecomte, P.B.A., Rigo, M.: Numeration systems on a regular language. Theory Comput. Syst. 34(1), 27–44 (2001). https://doi.org/10.1007/s002240010014

    Article  MathSciNet  MATH  Google Scholar 

  21. Lothaire, M.: Combinatorics on words. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1997). https://doi.org/10.1017/CBO9780511566097, corrected reprint of the 1983 original

  22. Mantaci, S., Restivo, A., Romana, G., Rosone, G., Sciortino, M.: A combinatorial view on string attractors. Theoret. Comput. Sci. 850, 236–248 (2021). https://doi.org/10.1016/j.tcs.2020.11.006

    Article  MathSciNet  MATH  Google Scholar 

  23. Parry, W.: On the \(\beta \)-expansions of real numbers. Acta Math. Acad. Sci. Hungar. 11, 401–416 (1960). https://doi.org/10.1007/BF02020954

    Article  MathSciNet  MATH  Google Scholar 

  24. Restivo, A., Romana, G., Sciortino, M.: String attractors and infinite words. In: LATIN 2022: Theoretical informatics, vol. 13568. LNCS, pp. 426–442. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-20624-5_26

  25. Reutenauer, C.: Mots de Lyndon généralisés. Sém. Lothar. Combin. 54, Art. B54h, 16 (2005/07)

    Google Scholar 

  26. Rigo, M.: Formal languages, automata and numeration systems. 2. Applications to recognizability and decidability. Networks and Telecommunications Series, ISTE, London; John Wiley & Sons Inc, Hoboken, NJ (2014). https://doi.org/10.1002/9781119042853

  27. Schaeffer, L., Shallit, J.: String attractor for automatic sequences, preprint available at arXiv:2012.06840 (2022)

  28. Shallit, J.: The logical approach to automatic sequences. Exploring combinatorics on words with Walnut, Lond. Math. Soc, vol. 482. Lecture Notes Series. Cambridge University Press, Cambridge (2023). https://doi.org/10.1017/9781108775267

Download references

Acknowledgements

France Gheeraert is a Research Fellow of the FNRS. Manon Stipulanti is supported by the FNRS Research grant 1.B.397.20F. We warmly thank M. Rigo and S. Kreczman for useful discussions on numeration systems, especially for indicating [9] and [17] respectively.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Liège, Liège, Belgium

    France Gheeraert & Manon Stipulanti

  2. Dipartimento di Matematica e Informatica, Università di Palermo, Palermo, Italy

    Giuseppe Romana

Authors
  1. France Gheeraert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Giuseppe Romana
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Manon Stipulanti
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to France Gheeraert .

Editor information

Editors and Affiliations

  1. Aix-Marseille University, Marseille, France

    Anna Frid

  2. Loughborough University, Loughborough, UK

    Robert Mercaş

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gheeraert, F., Romana, G., Stipulanti, M. (2023). String Attractors of Fixed Points of k-Bonacci-Like Morphisms. In: Frid, A., Mercaş, R. (eds) Combinatorics on Words. WORDS 2023. Lecture Notes in Computer Science, vol 13899. Springer, Cham. https://doi.org/10.1007/978-3-031-33180-0_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-33180-0_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-33179-4

  • Online ISBN: 978-3-031-33180-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation