Scanning Pictures the Boustrophedon Way

  • Henning Fernau
  • Meenakshi ParamasivanEmail author
  • Markus L. Schmid
  • D. Gnanaraj Thomas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9448)


We are introducing and discussing finite automata working on rectangular-shaped arrays (i.e., pictures) in a boustrophedon reading mode. We prove close relationships with the well-established class of regular matrix (picture) languages. We derive several combinatorial, algebraic and decidability results for the corresponding class of picture languages. For instance, we show pumping and interchange lemmas for our picture language class. We also explain similarities and differences to the status of decidability questions for classical finite string automata. For instance, the non-emptiness problem for our picture-processing automaton model(s) turns out to be NP-complete. Finally, we sketch possible applications to character recognition.


Regular Language Finite Automaton Membership Problem Picture Processing Deterministic Finite Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Amar, V., Putzolu, G.: On a family of linear grammars. Inf. Cont. 7, 283–291 (1964). (Now Information and Computation)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Dassow, J.: Grammatical picture generation (2007).
  3. 3.
    Fernau, H.: Even linear simple matrix languages: formal language properties and grammatical inference. Theor. Comput. Sci. 289, 425–489 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Fernau, H., Freund, R.: Bounded parallelism in array grammars used for character recognition. In: Perner, P., Wang, P., Rosenfeld, A. (eds.) SSPR 1996. LNCS, vol. 1121, pp. 40–49. Springer, Heidelberg (1996) CrossRefGoogle Scholar
  5. 5.
    Fernau, H., Freund, R., Holzer, M.: Character recognition with \(k\)-head finite array automata. In: Amin, A., Dori, D., Pudil, P., Freeman, H. (eds.) SPR 1998 and SSPR 1998. LNCS, vol. 1451, pp. 282–291. Springer, Heidelberg (1998) CrossRefGoogle Scholar
  6. 6.
    Fernau, H., Sempere, J.M.: Permutations and control sets for learning non-regular language families. In: Oliveira, A.L. (ed.) ICGI 2000. LNCS (LNAI), vol. 1891, pp. 75–88. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  7. 7.
    Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. III, pp. 215–267. Springer, Berlin (1997)CrossRefGoogle Scholar
  8. 8.
    Krithivasan, K., Siromoney, R.: Array automata and operations on array languages. Int. J. Comput. Math. 4(A), 3–30 (1974)zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Krithivasan, K., Siromoney, R.: Characterizations of regular and context-free matrices. Int. J. Comput. Math. 4(A), 229–245 (1974)zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Lange, K.J., Rossmanith, P.: The emptiness problem for intersections of regular languages. In: Havel, I.M., Koubek, V. (eds.) MFCS 1992. LNCS, vol. 629, pp. 346–354. Springer, Heidelberg (1992) CrossRefGoogle Scholar
  11. 11.
    Nagy, B.: On a hierarchy of \({5^{\prime }}\) \(\rightarrow \) \({3^{\prime }}\) sensing Watson-Crick finite automata languages. J. Logic Comput. 23(4), 855–872 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Niedermeier, R., Reinhardt, K., Sanders, P.: Towards optimal locality in mesh-indexings. Discrete Appl. Math. 117, 211–237 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Fernau, H., Freund, R., Holzer, M.: Regulated array grammars of finite index. In: Păun, G., Salomaa, A. (eds.) Grammatical Models of Multi-Agent Systems, pp. 157–181 (Part I) and 284–296 (Part II). Gordon and Breach, London (1999)Google Scholar
  14. 14.
    Sagan, H.: Space-Filling Curves. Springer, Heidelberg (1994)zbMATHCrossRefGoogle Scholar
  15. 15.
    Siromoney, G., Siromoney, R., Krithivasan, K.: Abstract families of matrices and picture languages. Comput. Graph. Image Process. 1, 284–307 (1972)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Siromoney, G., Siromoney, R., Krithivasan, K.: Picture languages with array rewriting rules. Inf. Control 22(5), 447–470 (1973). (Now Information and Computation)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Siromoney, G., Siromoney, R., Krithivasan, K.: Array grammars and kolam. Comput. Graph. Image Process. 3, 63–82 (1974)CrossRefGoogle Scholar
  18. 18.
    Siromoney, R.: On equal matrix languages. Inf. Control 14, 133–151 (1969). (Now Information and Computation)CrossRefGoogle Scholar
  19. 19.
    Siromoney, R., Mathew, L., Subramanian, K.G., Dare, V.R.: Learning of recognizable picture languages. In: Nakamura, A., Nivat, M., Saoudi, A., Wang, P.S.P., Inoue, K. (eds.) ICPIA 1992. LNCS, vol. 654, pp. 247–259. Springer, Heidelberg (1992) CrossRefGoogle Scholar
  20. 20.
    Siromoney, R., Subramanian, K.G.: Space-filling curves and infinite graphs. In: Ehrig, H., Nagl, M., Rozenberg, G. (eds.) Graph Grammars 1982. LNCS, vol. 153, pp. 380–391. Springer, Heidelberg (1983) CrossRefGoogle Scholar
  21. 21.
    Subramanian, K.G., Revathi, L., Siromoney, R.: Siromoney array grammars and applications. Int. J. Pattern Recogn. Artif. Intell. 3, 333–351 (1989)CrossRefGoogle Scholar
  22. 22.
    Takada, Y.: Learning even equal matrix languages based on control sets. In: Nakamura, A., Nivat, M., Saoudi, A., Wang, P.S.P., Inoue, K. (eds.) ICPIA 1992. LNCS, vol. 654, pp. 274–289. Springer, Heidelberg (1992) CrossRefGoogle Scholar
  23. 23.
    Witten, I.H., Wyvill, B.: On the generation and use of space-filling curves. Softw. Pract. Experience 13, 519–525 (1983)zbMATHCrossRefGoogle Scholar
  24. 24.
    Yanagisawa, K., Nagata, S.: Fundamental study on design system of kolam pattern. Forma 22, 31–46 (2007)MathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Henning Fernau
    • 1
  • Meenakshi Paramasivan
    • 1
    Email author
  • Markus L. Schmid
    • 1
  • D. Gnanaraj Thomas
    • 2
  1. 1.Fachbereich 4 – Abteilung InformatikUniversität TrierTrierGermany
  2. 2.Department of MathematicsMadras Christian CollegeChennaiIndia

Personalised recommendations