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On Some Properties of the Language of 2-Collapsing Words

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Developments in Language Theory (DLT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3572))

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Abstract

We present two new results on 2-collapsing words. First, we show that the language of all 2-collapsing words over 2 letters is not context-free. Second, we prove that the length of a 2-collapsing word over an arbitrary finite alphabet Σ is at least 2|Σ|2 thus improving the previously known lower bound |Σ|2 + 1.

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References

  1. Almeida, J., Volkov, M.V.: Profinite identities for finite semigroups whose subgroups belong to a given pseudovariety. J. Algebra Appl. 2, 137–163 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Ananichev, D.S., Cherubini, A., Volkov, M.V.: An inverse automata algorithm. In: Ito, M., Toyama, M. (eds.) DLT 2002. LNCS, vol. 2450, pp. 270–282. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Ananichev, D.S., Cherubini, A., Volkov, M.V.: Image reducing words and subgroups of free groups. Theor. Comp. Sci. 307, 77–92 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ananichev, D.S., Petrov, I.V.: Quest for short synchronizing words and short collapsing words. In: Proc. 4th Int. Conf., pp. 411–418. Univ. of Turku, Turku (2003)

    Google Scholar 

  5. Ananichev, D.S., Volkov, M.V.: Collapsing words vs. Synchronizing words. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds.) DLT 2001. LNCS, vol. 2295, pp. 166–174. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  6. Berstel, J.: Transductions and Context-free Languages. Teubner, Stuttgart (1969)

    Google Scholar 

  7. Lyndon, R., Schupp, P.: Combinatorial Group Theory. Springer, Berlin (1977)

    MATH  Google Scholar 

  8. Hall, M.: A topology for free groups and related groups. Ann. Math. 52, 127–139 (1950)

    Article  Google Scholar 

  9. Margolis, S.W., Pin, J.-E., Volkov, M.V.: Words guaranteeing minimum image. Int. J. Foundations Comp. Sci. 15, 259–276 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ogden, W.: A helpful result for proving inherent ambiguity. Math. Systems Theory 2, 191–194 (1968)

    Article  MATH  MathSciNet  Google Scholar 

  11. Pöschel, R., Sapir, M.V., Sauer, N., Stone, M.G., Volkov, M.V.: Identities in full transformation semigroups. Algebra Universalis 31, 580–588 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  12. Sauer, N., Stone, M.G.: Composing functions to reduce image size. Ars Combinatoria 31, 171–176 (1991)

    MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Ural State University, 620083, Ekaterinburg, Russia

    E. V. Pribavkina

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  1. E. V. Pribavkina
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Editors and Affiliations

  1. Dipartimento di Informatica e Applicazioni, Università di Salerno, via Ponte Don Melillo, 84084, Fisciano, SA, Italy

    Clelia De Felice

  2. Dipartimento di Matematica ed Applicazioni, Università di Palermo, Via Archirafi, 34, 90123, Palermo, Italy

    Antonio Restivo

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© 2005 Springer-Verlag Berlin Heidelberg

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Pribavkina, E.V. (2005). On Some Properties of the Language of 2-Collapsing Words. In: De Felice, C., Restivo, A. (eds) Developments in Language Theory. DLT 2005. Lecture Notes in Computer Science, vol 3572. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505877_33

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  • DOI: https://doi.org/10.1007/11505877_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26546-7

  • Online ISBN: 978-3-540-31682-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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