Parallel Contextual Array Insertion Deletion Grammar

  • D. G. ThomasEmail author
  • S. James Immanuel
  • Atulya K. Nagar
  • Robinson Thamburaj
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11255)


We introduce a new grammar, called parallel contextual array insertion deletion grammar and show that it has a strictly higher generative power than a system generating recognizable 2D-picture language and Siromoney context-sensitive matrix grammar.


Rectangular array Parallel contextual array grammar Insertion and deletion 



The authors are thankful to Prof. Henning Fernau (Fachbereich 4-Abteilung Informatik, Universität Trier, D-54286 Trier, Germany) for his valuable input to this paper. A four page abstract of this paper (not refereed) has appeared in the technical report of Theorietag 2017 held at Bonn, Germany during September 18–22, 2017. (See: [PDF] Theorietag 2017-Uni.Trier, page 41–44).


  1. 1.
    Ehrenfeucht, A., P\(\breve{\text{a}}\)un, Gh., Rozenberg, G.: Contextual grammars and formal languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, pp. 237–293. Springer, Heidelberg (1997). Scholar
  2. 2.
    Fernau, H., Freund, R., Schmid, M.L., Subramanian, K.G., Wielderhold, P.: Contextual array grammars and array P systems. Ann. Math. Artif. Intell. 75, 5–26 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Fernau, H., Paramasivan, M., Schmid, M.L., Thomas, D.G.: Some picture processing based on finite automata and regular grammars. J. Comput. Syst. Sci. 95, 232–258 (2018)CrossRefGoogle Scholar
  4. 4.
    Freund, R.: Array grammars. Technical report No. 15/00. Universitat Rovirai Virgili (2000)Google Scholar
  5. 5.
    Freund, R., P\(\breve{\text{ a }}\)un, Gh., Rozenberg, G.: Contextual array grammars. In: Subramanian, K.G., Rangarajan, K., Mukund, M. (eds.) Formal Models, Languages and Application Series in Machine Perception and Artificial Intelligence, vol. 66, pp. 112–136. World Scientific (2007)Google Scholar
  6. 6.
    Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 3, pp. 215–267. Springer, Heidelberg (1997). Scholar
  7. 7.
    Giammarresi, D., Restivo, A.: Recognizable picture languages. Int. J. Pattern Recognit. Artif. Intell. 6, 241–256 (1992)CrossRefGoogle Scholar
  8. 8.
    Helen Chandra, P., Subramanian, K.G., Thomas, D.G.: Parallel contextual array grammars and languages. Electron. Not. Discrete Math. 12, 106–117 (2003)MathSciNetCrossRefGoogle Scholar
  9. 9.
    James Immanuel, S., Thomas, D.G., Thamburaj, R., Nagar, A.K.: Parallel contextual array insertion deletion P system. In: Brimkov, V.E., Barneva, R.P. (eds.) IWCIA 2017. LNCS, vol. 10256, pp. 170–183. Springer, Cham (2017). Scholar
  10. 10.
    Krithivasan, K., Balan, M.S., Rama, R.: Array contextual grammars. In: Martin-Vide,C., P\(\breve{\text{ a }}\)un, Gh. (eds.) Recent Topics in Mathematical and Computational Linguistics, pp. 154–168. The Publishing House of the Romanian Academy (2000)Google Scholar
  11. 11.
    Marcus, S.: Contextual grammars. Rev. Roum. Math. Pures et Appl. 14(10), 1525–1534 (1969)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Matz, O.: Regular expressions and context-free grammars for picture languages. In: Reischuk, R., Morvan, M. (eds.) STACS 1997. LNCS, vol. 1200, pp. 283–294. Springer, Heidelberg (1997). Scholar
  13. 13.
    P\(\breve{\text{ a }}\)un, Gh.: Marcus Contextual Grammars. Kluwer, Dordrecht (1997)Google Scholar
  14. 14.
    Pradella, M., Cherubini, A., Reghizzi, C.: A unifying approach to picture grammars. Inf. Comput. 209, 1246–1267 (2011)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Prusa, D.: Two dimensional languages. Ph.D. thesis. Charles University, Faculty of Mathematics and Physics, Czech Republic (2004)Google Scholar
  16. 16.
    Rama, R., Smitha, T.A.: Some results on array contextual grammars. Int. J. Pattern Recognit. Artif. Intell. 14, 537–550 (2000)Google Scholar
  17. 17.
    Rosenfeld, A.: Isotonic grammars, parallel grammars and picture grammars. In: Michie, D., Meltzer, D. (eds.) Machine Intelligence VI, pp. 281–294. University of Edinburgh Press, Scotland (1971)Google Scholar
  18. 18.
    Rosenfeld, A.: Picture Languages: Formal Models for Picture Recognition. Academic Press, Cambridge (1979)zbMATHGoogle Scholar
  19. 19.
    Siromoney, G., Siromoney, R., Krithivasan, K.: Abstract families of matrices and picture languages. Comput. Graph. Image Process. 1, 234–307 (1972)MathSciNetzbMATHGoogle Scholar
  20. 20.
    Siromoney, G., Siromoney, R., Krithivasan, K.: Picture languages with array rewriting rules. Inf. Control 22, 447–470 (1973)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Subramanian, K.G., Van, D.L., Chandra, P.H., Quyen, N.D.: Array grammars with contextual operations. Fund. Info. 83, 411–428 (2008)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Subramanian, K.G., Revathi, L., Siromoney, R.: Siromoney array grammars and applications. Int. J. Pattern Recognit. Artif. Intell. 3, 333–351 (1989)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • D. G. Thomas
    • 1
    Email author
  • S. James Immanuel
    • 2
  • Atulya K. Nagar
    • 3
  • Robinson Thamburaj
    • 2
  1. 1.Department of Science and HumanitiesSaveetha School of Engineering, SIMATSChennaiIndia
  2. 2.Department of MathematicsMadras Christian CollegeTambaram, ChennaiIndia
  3. 3.Department of Mathematics and Computer ScienceLiverpool Hope UniversityLiverpoolUK

Personalised recommendations