Algorithms Based on Finite Automata for Testing of Omega-Codes

  • Thang Dang Quyet
  • Han Nguyen Dinh
  • Huy Phan Trung
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 164)


We establish an algorithm that, given as input a finite automaton recognizing a regular language L, decides whether L is an ω-code. In case the input is a non-deterministic finite automaton, the algorithm has time complexity O(n 4). In special case, if the input is a deterministic finite automaton, the time complexity of the algorithm is reduced to O(n 2), where n is the number of states of that automaton.


Deterministic automata Bipolar Quadratic algorithm Omega-code 


  1. 1.
    Augros, X., Litovsky, I.: Algorithm to test rational ω-codes. In: Proceedings of the Conference of The Mathematical Foundation of Informatics. pp. 23–37. World Scientific (Oct 1999)Google Scholar
  2. 2.
    Béal, M.P., Perrin, D.: Codes, unambiguous automata and sofic systems. Theoret. Comput. Sci. 356, 6–13 (2006)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Berman, K.A., Paul, J.L.: Algorithms—sequential, parallel, and distributed. Thomson Learning, Inc., USA (2005)Google Scholar
  4. 4.
    Berstel, J., Perrin, D.: Theory of codes. Academic Press Inc, New York (1985)MATHGoogle Scholar
  5. 5.
    Carton, O., Perrin, D., Pin, J.E.: Automata and semigroups recognizing infinite words. Logic and Automata, History and perspectives. In: Flum, J., Grädel, E., Wilke, T. (eds.) Amsterdam University Press. pp. 133–167 (2007)Google Scholar
  6. 6.
    Devolder, J., Latteux, M., Litovsky, I., Staiger, L.: Codes and infinite words. Acta Cybernetica 11(4), 241–256 (1994)MathSciNetMATHGoogle Scholar
  7. 7.
    Huy, P.T., Van, D.L.: On non-ambiguous Büchi V-automata. In: Proceedings of the Third Asian Mathematical Conference. pp. 224–233. World Scientific (2002)Google Scholar
  8. 8.
    Lallement, G.: Semigroups and combinational applications. Wiley, New York (1979)Google Scholar
  9. 9.
    Mohri, M.: Edit-distance of weighted automata: general definitions and algorithms. Int. J. Found. Comput. Sci. 14(6), 957–982 (2003)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Mohri, M., Pereira, F., Riley, M.: Speech recognition with weighted finite-state transducers. Springer, Heidelberg (2007)Google Scholar
  11. 11.
    Perrin, D., Pin, J. E.: Infinite words. Pure and applied mathematics, vol. 141. Elsevier (2004)Google Scholar
  12. 12.
    Sedgewick, R.: Algorithms in C++, Part 5: Graph algorithms. Addition-wesley, Pearson Education, Inc, USA (2002)Google Scholar

Copyright information

© Springer Science+Business Media Dortdrecht 2012

Authors and Affiliations

  • Thang Dang Quyet
    • 1
  • Han Nguyen Dinh
    • 2
  • Huy Phan Trung
    • 3
  1. 1.Nam Dinh University of Technology and EducationNam DinhVietnam
  2. 2.Hung Yen University of Technology and EducationHung YenVietnam
  3. 3.Hanoi University of Science and TechnologyHa NoiVietnam

Personalised recommendations