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2-Synchronizing Words

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Language and Automata Theory and Applications (LATA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5196))

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Abstract

A word w over an alphabet Σ is n-synchronizing if it resets every (n + 1)-state synchronizing automaton over this alphabet. For a fixed n and Σ, n-synchronizing words can be recognized in polynomial time, yet no practical algorithm is known. In this paper we show that one cannot expect to find such an algorithm. We prove that the problem of recognizing 2-synchronizing words, where the input consists of a word and an alphabet, is co-NP-complete. We also show that the length of a 2-synchronizing word is at least 2|Σ|2, which improves the lower bound known so far.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Ananichev, D.S., Volkov, M.V.: Synchronizing monotonic automata. Theor. Comput. Sci. 327(1), 225–239 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  3. 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 

  4. Ananichev, D.S., Petrov, I.V., Volkov, M.V.: Collapsing words: A Progress Report. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 11–21. Springer, Heidelberg (2005)

    Google Scholar 

  5. Černý, J.: Poznámka k. homogénnym experimentom s konecnými automatmi. Mat. fyz. čas SAV 14, 208–215 (1964)

    MATH  Google Scholar 

  6. Cherubini, A., Gawrychowski, P., Kisielewicz, A., Piochi, B.: A combinatorial approach to collapsing words. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 256–266. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Kari, J.: Synchronizing finite automata on Eulerian digraphs. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 432–438. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  8. Mateescu, A., Salomaa, A.: Many-valued truth functions, Černy’y’s conjecture and road coloring. EATCS Bull. 68, 134–150 (1999)

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  10. Alon, N.: Combinatorial Nullstellensatz. Comb. Probab. Comput. 8, 7–29 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Pribavkina, E.V.: On Some Properties of the Language of 2-Collapsing Words. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572. Springer, Heidelberg (2005)

    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. Institute of Computer Science, University of Wrocław, ul. Joliot-Curie 15, 50-383, Wrocław, Poland

    Paweł Gawrychowski

  2. Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2, 50-384, Wrocław, Poland

    Andrzej Kisielewicz

Authors
  1. Paweł Gawrychowski
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  2. Andrzej Kisielewicz
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Editor information

Editors and Affiliations

  1. Research Group on Mathematical Linguistics, Rovira i Virgili University, Plaza Imperial Tàrraco 1, 43005, Tarragona, Spain

    Carlos Martín-Vide

  2. Fachbereich Elektrotechnik/Informatik, Universität Kassel, Wilhelmshöher Allee 73, 34121, Kassel, Germany

    Friedrich Otto

  3. Fachbereich 4, Abteilung Informatik/Wirtschaftsinformatik, Universität Trier, Campus II, Gebäude H, 54286, Trier, Germany

    Henning Fernau

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Gawrychowski, P., Kisielewicz, A. (2008). 2-Synchronizing Words. In: Martín-Vide, C., Otto, F., Fernau, H. (eds) Language and Automata Theory and Applications. LATA 2008. Lecture Notes in Computer Science, vol 5196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88282-4_21

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  • DOI: https://doi.org/10.1007/978-3-540-88282-4_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88281-7

  • Online ISBN: 978-3-540-88282-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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