On Recognizable Infinite Array Languages

  • S. Gnanasekaran
  • V. R. Dare
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)


A recognizable infinite array language or recognizable ωω-language is defined as the image of a local ωω-language by an alphabetic morphism. Here, we introduce Wang systems for ωω-languages and prove that the class of ωω-languages obtained by Wang systems is the same as the class of recognizable ωω-languages. We give automata characterization to the recognizable ωω-languages. We provide an algorithm for learning recognizable infinite array languages from positive data and restricted superset queries.


array prefix local language recognizable array language on-line tesselation automaton learning 


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  1. 1.
    Angluin, D.: Inductive inference of formal languages from positive data. Information and Control 45, 117–135 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Angluin, D.: Queries and concept learning. Machine Learning 2, 319–342 (1988)Google Scholar
  3. 3.
    Culik II, K., Kari, J.: An aperiodic set of Wang cubes. LNCS, vol. 1046, pp. 137–147. Springer, Heidelberg (1996)Google Scholar
  4. 4.
    Dare, V.R., Subramanian, K.G., Thomas, D.G., Siromoney, R.: Infinite arrays and recognizability. International Journal of Pattern Recognition and Artificial Intelligence 14(4), 525–536 (2000)CrossRefGoogle Scholar
  5. 5.
    De Prophetis, L., Varricchio, S.: Recognizability of rectangular pictures by Wang systems. Journal of Automata, Languages and Combinatorics 2(4), 269–288 (1997)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Eilenberg, S.: Automata, Languages and Machines, vol. A. Academic Press, New York (1974)zbMATHGoogle Scholar
  7. 7.
    Giammerresi, D., Restivo, A.: Recognizable picture languages. Int. J. Pattern Recognition and Artificial Intelligence 6, 241–256 (1992)CrossRefGoogle Scholar
  8. 8.
    Gnanasekaran, S., Dare, V.R.: Infinite arrays and domino systems. Electronic Notes in Discrete Mathematics 12 (2003)Google Scholar
  9. 9.
    Gold, E.M.: Language identification in the limit. Information and Control 10, 447–474 (1967)zbMATHCrossRefGoogle Scholar
  10. 10.
    Inoue, K., Nakamura, A.: Some properties of two-dimensional on-line tesselation acceptor. Inf. Sci. 13, 95–121 (1977)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Latteux, M., Simplot, D.: Theoretical Computer Science 178, 275–283 (1997)Google Scholar
  12. 12.
    Saoudi, A., Yokomori, T.: Learning local and recognizable ω-languages and monodic logic programs. In: Proc. Euro COLT 1993 (1993)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • S. Gnanasekaran
    • 1
  • V. R. Dare
    • 2
  1. 1.Department of MathematicsPeriyar Arts CollegeCuddaloreIndia
  2. 2.Department of MathematicsMadras Christian CollegeTambaram, ChennaiIndia

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