Skip to main content

Online Tessellation Automaton Recognizing Various Classes of Convex Polyominoes

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6026))

Abstract

A polyomino is a finite connected union of cells having no cut points. Tiling and Wang recognizability of convex polyominoes have been studied in detail by De Carli et al. In this paper we define 2D polyomino online tessellation automaton to recognize a class of polyominoes and prove that the family of various classes of polyominoes recognized by tiling systems and 2D-polyomino online tessellation automata coincide. We also study the recognizability of convex polyominoes by domino systems.

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

Buying options

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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blum, M., Hewitt, C.: Automata on a 2-dimensional tape. In: IEEE Symposium on Switching and Automata Theory, pp. 155–160 (1967)

    Google Scholar 

  2. De Carli, F., Frosini, A., Rinaldi, S., Vuillon, L.: How to construct convex polyominoes on DNA Wang tiles? LAMA report, Lama-Univ. Savoie, France (2009)

    Google Scholar 

  3. De Carli, F., Frosini, A., Rinaldi, S., Vuillon, L.: On the tiling system recognizability of various classes of convex polyominoes. Annals of Combinatorics 13, 169–191 (2009)

    Article  MathSciNet  Google Scholar 

  4. Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Salomaa, A., Rozenberg, G. (eds.) Handbook of Formal Languages, vol. 3, pp. 215–267. Springer, Heidelberg (1997)

    Google Scholar 

  5. Castiglione, G., Vaglica, R.: Recognizable picture languages and polyominoes. In: Bozapalidis, S., Rahonis, G. (eds.) CAI 2007. LNCS, vol. 4728, pp. 160–171. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  6. Inoue, K., Nakamura, A.: Some properties of two-dimensional on-line tessellation acceptors. Information Sciences 13, 95–121 (1977)

    Article  MathSciNet  Google Scholar 

  7. Latteux, M., Simplot, D.: Recognizable picture languages and domino tiling. Theoretical Computer Science 178, 275–283 (1997)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Geetha, H., Thomas, D.G., Kalyani, T. (2010). Online Tessellation Automaton Recognizing Various Classes of Convex Polyominoes. In: Barneva, R.P., Brimkov, V.E., Hauptman, H.A., Natal Jorge, R.M., Tavares, J.M.R.S. (eds) Computational Modeling of Objects Represented in Images. CompIMAGE 2010. Lecture Notes in Computer Science, vol 6026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12712-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12712-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12711-3

  • Online ISBN: 978-3-642-12712-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics