Skip to main content

On the Synchronization of Planar Automata

  • Conference paper
  • First Online:
Language and Automata Theory and Applications (LATA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10792))

Abstract

Planar automata seems to be representative of the synchronizing behavior of deterministic finite state automata. We conjecture that Černy’s conjecture holds true, if and only if, it holds true for planar automata. We provide new (and old) evidence concerning the conjectured Č erny-universality of planar automata.

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

Access this chapter

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

References

  1. Ananichev, D., Gusev, V., Volkov, M.: Slowly synchronizing automata and digraphs. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 55–65. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15155-2_7

    Chapter  Google Scholar 

  2. Baeza-Yates, R.: Searching subsequences. Theor. Comput. Sci. 78(2), 363–376 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  3. Berlinkov, M.V.: On two algorithmic problems about synchronizing automata. In: Shur, A.M., Volkov, M.V. (eds.) DLT 2014. LNCS, vol. 8633, pp. 61–67. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09698-8_6

    Google Scholar 

  4. Book, R., Chandra, A.: Inherently nonplanar automata. Acta Inf. 6, 89–94 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  5. Černy, J.: Poznámka k homogénnym experimentom s konecnymi automatmi. Mat. fyz. cas SAV 14, 208–215 (1964)

    Google Scholar 

  6. Eppstein, D.: Reset sequences for monotonic automata. SIAM J. Comput. 19, 500–510 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Berlin (2006). https://doi.org/10.1007/3-540-29953-X

    MATH  Google Scholar 

  8. Gawrychowski, P., Straszak, D.: Strong inapproximability of the shortest reset word. In: Italiano, G.F., Pighizzini, G., Sannella, D.T. (eds.) MFCS 2015. LNCS, vol. 9234, pp. 243–255. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48057-1_19

    Chapter  Google Scholar 

  9. Guillemot, S.: Parameterized complexity and approximability of the longest compatible sequence problem. Discret. Optim. 8(1), 50–60 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Montoya, J., Nolasco, C.: On the synchronization of small sets of states. Appl. Math. Sci. 11(44), 2151–2173 (2017)

    Google Scholar 

  11. Olschewski, J., Ummels, M.: The complexity of finding reset words in finite automata. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 568–579. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15155-2_50

    Chapter  Google Scholar 

Download references

Acknowledgement

The second author would like to thank the support provided by Universidad Nacional de Colombia through the project Hermes 8943 (32083).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Andres Montoya .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Andres Montoya, J., Nolasco, C. (2018). On the Synchronization of Planar Automata. In: Klein, S., Martín-Vide, C., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2018. Lecture Notes in Computer Science(), vol 10792. Springer, Cham. https://doi.org/10.1007/978-3-319-77313-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-77313-1_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77312-4

  • Online ISBN: 978-3-319-77313-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics