Skip to main content
SpringerLink
Log in

Regular Ideal Languages and Synchronizing Automata

  • Conference paper
Combinatorics on Words

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8079))

Abstract

We introduce the notion of reset left regular decomposition of an ideal regular language and we prove that there is a one-to-one correspondence between these decompositions and strongly connected synchronizing automata. We show that each ideal regular language has at least a reset left regular decomposition. As a consequence each ideal regular language is the set of synchronizing words of some strongly connected synchronizing automaton. Furthermore, this one-to-one correspondence allows us to formulate Černý’s conjecture in a pure language theoretic framework.

Work partialy supported by the European Regional Development Fund through the programme COMPETE and by the Portuguese Government through the FCT – Fundação para a Ciência e a Tecnologia under the project PEst-C/MAT/UI0144/2011 and CANTE-PTDC/EIA-CCO/101904/2008.

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 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 72.00
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gusev, V., Maslennikova, M., Pribavkina, E.: Principal ideal languages and synchronizing automata. In: Halava, V., Karhumaki, J., Matiyasevich, Y. (eds.) RuFiDimII. TUCS Lecture Notes, vol. 17 (2012)

    Google Scholar 

  2. Gusev, V.V., Maslennikova, M.I., Pribavkina, E.V.: Finitely generated ideal languages and synchronizing automata. In: Karhumäki, J., Lepistö, A., Zamboni, L. (eds.) WORDS 2013. LNCS, vol. 8079, pp. 143–153. Springer, Heidelberg (2013)

    Google Scholar 

  3. Maslennikova, M.: Reset complexity of ideal languages. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Špánek, R., Turán, G. (eds.) Proc. Int. Conf. SOFSEM 2012, vol. II, pp. 33–44. Institute of Computer Science Academy of Sci- ences of the Czech Republic (2012)

    Google Scholar 

  4. Pin, J.E.: On two combinatorial problems arising from automata theory. Ann. Discrete Math. 17, 535–548 (1983)

    MATH  Google Scholar 

  5. Pribavkina, E.V., Rodaro, E.: Finitely generated synchronizing automata. In: Dediu, A.H., Ionescu, A.M., Martín-Vide, C. (eds.) LATA 2009. LNCS, vol. 5457, pp. 672–683. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Pribavkina, E.V., Rodaro, E.: State complexity of prefix, suffix, bifix and infix operators on regular languages. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds.) DLT 2010. LNCS, vol. 6224, pp. 376–386. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  7. Pribavkina, E.V., Rodaro, E.: Recognizing synchronizing automata with finitely many minimal synchronizing words is PSPACE-complete. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds.) CiE 2011. LNCS, vol. 6735, pp. 230–238. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Pribavkina, E.V., Rodaro, E.: State complexity of code operators. International Journal of Foundations of Computer Science 22(07), 1669–1681 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pribavkina, E.V., Rodaro, E.: Synchronizing automata with finitely many minimal synchronizing words. Information and Computation 209(3), 568–579 (2011), http://www.sciencedirect.com/science/article/pii/S0890540110002063

    Article  MathSciNet  MATH  Google Scholar 

  10. Rystsov, I.: Reset words for commutative and solvable automata. Theoretical Computer Science 172(1-2), 273–279 (1997), http://www.sciencedirect.com/science/article/pii/S0304397596001363

    Article  MathSciNet  MATH  Google Scholar 

  11. Černý, J.: Poznámka k homogénnym eksperimentom s konečnými automatami. Mat.-Fyz. Čas. Slovensk. Akad. Vied. 14, 208–216 (1964) (in slovak)

    MATH  Google Scholar 

  12. Volkov, M.V.: Synchronizing automata and the Černý conjecture. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 11–27. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centro de Matemática, Universidade do Porto, R. Campo Alegre 687, 4169-007, Porto, Portugal

    Rogério Reis & Emanuele Rodaro

Authors
  1. Rogério Reis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Emanuele Rodaro
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

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

    Juhani Karhumäki

  2. University of Turku, 20014, Turku, Finland

    Arto Lepistö

  3. FUNDIM, University of Turku, Finland

    Luca Zamboni

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Reis, R., Rodaro, E. (2013). Regular Ideal Languages and Synchronizing Automata. In: Karhumäki, J., Lepistö, A., Zamboni, L. (eds) Combinatorics on Words. Lecture Notes in Computer Science, vol 8079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40579-2_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40579-2_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40578-5

  • Online ISBN: 978-3-642-40579-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation