Skip to main content
SpringerLink
Log in

Separating Many Words by Counting Occurrences of Factors

  • Conference paper
  • First Online:
Developments in Language Theory (DLT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11647))

Included in the following conference series:

  • 335 Accesses

Abstract

For a given language L, we study the languages X such that for all distinct words \(u, v \in L\), there exists a word \(x \in X\) appearing a different number of times as a factor in u and in v. In particular, we are interested in the following question: For which languages L does there exist a finite language X satisfying the above condition? We answer this question for all regular languages and for all sets of factors of infinite words.

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

Similar content being viewed by others

Notes

  1. 1.

    http://wordlist.aspell.net/.

  2. 2.

    http://arxiv.org/abs/1905.07223.

References

  1. Ambainis, A., Bloch, S.A., Schweizer, D.L.: Delayed binary search, or playing twenty questions with a procrastinator. Algorithmica 32(4), 641–650 (2002). https://doi.org/10.1007/s00453-001-0097-4

    Article  MathSciNet  MATH  Google Scholar 

  2. Cassaigne, J., Karhumäki, J., Puzynina, S., Whiteland, M.A.: \(k\)-abelian equivalence and rationality. Fund. Inform. 154(1–4), 65–94 (2017). https://doi.org/10.3233/FI-2017-1553

    Article  MathSciNet  MATH  Google Scholar 

  3. Cassaigne, J., Karhumäki, J., Saarela, A.: On growth and fluctuation of \(k\)-abelian complexity. Eur. J. Combin. 65, 92–105 (2017). https://doi.org/10.1016/j.ejc.2017.05.006

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, J., Lü, X., Wu, W.: On the \(k\)-abelian complexity of the cantor sequence. J. Combin. Theory Ser. A 155, 287–303 (2018). https://doi.org/10.1016/j.jcta.2017.11.010

    Article  MathSciNet  MATH  Google Scholar 

  5. Currie, J., Petersen, H., Robson, J.M., Shallit, J.: Separating words with small grammars. J. Autom. Lang. Comb. 4(2), 101–110 (1999)

    MathSciNet  MATH  Google Scholar 

  6. Demaine, E.D., Eisenstat, S., Shallit, J., Wilson, D.A.: Remarks on separating words. In: Holzer, M., Kutrib, M., Pighizzini, G. (eds.) DCFS 2011. LNCS, vol. 6808, pp. 147–157. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22600-7_12

    Chapter  Google Scholar 

  7. Ginsburg, S., Spanier, E.H.: Bounded regular sets. Proc. Amer. Math. Soc. 17, 1043–1049 (1966). https://doi.org/10.2307/2036087

    Article  MathSciNet  MATH  Google Scholar 

  8. Goralčík, P., Koubek, V.: On discerning words by automata. In: Kott, L. (ed.) ICALP 1986. LNCS, vol. 226, pp. 116–122. Springer, Heidelberg (1986). https://doi.org/10.1007/3-540-16761-7_61

    Chapter  MATH  Google Scholar 

  9. Holub, V., Kortelainen, J.: On partitions separating words. Int. J. Algebra Comput. 21(8), 1305–1316 (2011). https://doi.org/10.1142/S0218196711006650

    Article  MathSciNet  MATH  Google Scholar 

  10. Karhumäki, J.: Generalized Parikh mappings and homomorphisms. Inf. Control 47(3), 155–165 (1980). https://doi.org/10.1016/S0019-9958(80)90493-3

    Article  MathSciNet  MATH  Google Scholar 

  11. Karhumäki, J., Saarela, A., Zamboni, L.Q.: On a generalization of Abelian equivalence and complexity of infinite words. J. Combin. Theory Ser. A 120(8), 2189–2206 (2013). https://doi.org/10.1016/j.jcta.2013.08.008

    Article  MathSciNet  MATH  Google Scholar 

  12. Karhumäki, J., Saarela, A., Zamboni, L.Q.: Variations of the Morse-Hedlund theorem for \(k\)-abelian equivalence. Acta Cybernet. 23(1), 175–189 (2017). https://doi.org/10.14232/actacyb.23.1.2017.11

    Article  MathSciNet  MATH  Google Scholar 

  13. Maňuch, J.: Characterization of a word by its subwords. In: Proceedings of the 4th DLT, pp. 210–219. World Scientific Publication (2000). https://doi.org/10.1142/9789812792464_0018

  14. Morse, M., Hedlund, G.A.: Symbolic dynamics. Amer. J. Math. 60(4), 815–866 (1938). https://doi.org/10.2307/2371264

    Article  MathSciNet  MATH  Google Scholar 

  15. Pelc, A.: Solution of Ulam’s problem on searching with a lie. J. Combin. Theory Ser. A 44(1), 129–140 (1987). https://doi.org/10.1016/0097-3165(87)90065-3

    Article  MathSciNet  MATH  Google Scholar 

  16. Place, T., Zeitoun, M.: Separating regular languages with first-order logic. Log. Methods Comput. Sci. 12(1), 31 (2016). https://doi.org/10.2168/LMCS-12(1:5)2016. Paper No. 5

    Article  MathSciNet  MATH  Google Scholar 

  17. Richomme, G., Saari, K., Zamboni, L.Q.: Abelian complexity of minimal subshifts. J. Lond. Math. Soc. 83(1), 79–95 (2011). https://doi.org/10.1112/jlms/jdq063

    Article  MathSciNet  MATH  Google Scholar 

  18. Robson, J.M.: Separating strings with small automata. Inform. Process. Lett. 30(4), 209–214 (1989). https://doi.org/10.1016/0020-0190(89)90215-9

    Article  MathSciNet  MATH  Google Scholar 

  19. Vyalyĭ, M.N., Gimadeev, R.A.: On separating words by the occurrences of subwords. Diskretn. Anal. Issled. Oper. 21(1), 3–14 (2014). https://doi.org/10.1134/S1990478914020161

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Turku, 20014, Turku, Finland

    Aleksi Saarela

Authors
  1. Aleksi Saarela
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aleksi Saarela .

Editor information

Editors and Affiliations

  1. University of Warsaw, Warsaw, Poland

    Piotrek Hofman

  2. University of Warsaw, Warsaw, Poland

    Michał Skrzypczak

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

Saarela, A. (2019). Separating Many Words by Counting Occurrences of Factors. In: Hofman, P., Skrzypczak, M. (eds) Developments in Language Theory. DLT 2019. Lecture Notes in Computer Science(), vol 11647. Springer, Cham. https://doi.org/10.1007/978-3-030-24886-4_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-24886-4_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24885-7

  • Online ISBN: 978-3-030-24886-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation