Skip to main content

Rectangular Arrays and Petri Nets

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNIP,volume 7655)

Abstract

Array Token Petri Net Structure (ATPNS) to generate rectangular arrays has been defined in [6]. We prove that this model generate the regular array languages. By introducing a control on the firing sequence, we have shown that, ATPNS with inhibitor arcs generate the context-free and context-sensitive array languages. Comparisons with other classes of array languages have been made.

Keywords

  • Array token
  • Catenation
  • Inhibitor arcs
  • Petri net
  • Picture languages

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • 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. Baker, H.G.: Petri net languages. Computation Structures Group Memo 124, Project MAC. MIT, Cambridge (1972)

    Google Scholar 

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

    Google Scholar 

  3. Hack, M.: Petri net languages. Computation Structures Group Memo 124, Project MAC. MIT (1975)

    Google Scholar 

  4. Peterson, J.L.: Petri Net Theory and Modeling of Systems. Prentice Hall, Inc., Englewood Cliffs (1981)

    Google Scholar 

  5. Lalitha, D., Rangarajan, K.: Column and row catenation petri net systems. In: Proceedings of the Fifth IEEE International Conference on Bio-Inspired Computing: Theories and Applications, pp. 1382–1387 (2010)

    Google Scholar 

  6. Lalitha, D., Rangarajan, K.: An application of array token Petri nets to clustering analysis for syntactic patterns. International Journal of Computer Applications 42(16), 21–25 (2012)

    CrossRef  Google Scholar 

  7. Rosenfeld, A., Siromoney, R.: Picture languages - A survey. Languages of Design 1(3), 229–245 (1993)

    Google Scholar 

  8. Shirley Gloria, D.K., Immanuel, B., Rangarajan, K.: Parallel context-free string-token Petri nets. International Journal of Pure and Applied Mathematics 59(3), 275–289 (2010)

    MathSciNet  MATH  Google Scholar 

  9. Siromoney, R.: Advances in Array Languages. In: Ehrig, H., Nagl, M., Rosenfeld, A., Rozenberg, G. (eds.) Graph Grammars 1986. LNCS, vol. 291, pp. 549–563. Springer, Heidelberg (1987)

    CrossRef  Google Scholar 

  10. Siromoney, R., Siromoney, G.: Extended controlled table L-arrays. Information and Control 35, 119–138 (1977)

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Siromoney, G., Siromoney, R., Kamala, K.: Picture languages with array rewriting rules. Information and Control 22, 447–470 (1973)

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. Siromoney, G., Siromoney, R., Kamala, K.: Array grammars and kolam. Computer Graphics and Image Processing 3(1), 63–82 (1974)

    CrossRef  Google Scholar 

  13. Subramanian, K.G., Rosihan, M., Ali, G.M., Nagar, A.K.: Pure 2D picture grammars and languages. Discrete Applied Mathematics 157(16), 3401–3411 (2009)

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Wang, P.S.P.: An application of array grammars to clustering analysis for syntactic patterns. Pattern Recognition 17(4), 441–451 (1984)

    CrossRef  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lalitha, D., Rangarajan, K., Thomas, D.G. (2012). Rectangular Arrays and Petri Nets. In: Barneva, R.P., Brimkov, V.E., Aggarwal, J.K. (eds) Combinatorial Image Analaysis. IWCIA 2012. Lecture Notes in Computer Science, vol 7655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34732-0_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34732-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34731-3

  • Online ISBN: 978-3-642-34732-0

  • eBook Packages: Computer ScienceComputer Science (R0)