Programming and Computer Software

, Volume 31, Issue 6, pp 301–309 | Cite as

Test Sequence Construction Using Minimum Information on the Tested System

  • V. V. Kuliamin


In the paper, approaches to constructing test sequences are considered in the case where only admissible input actions on the system are known, whereas no information about the states of the system or transitions between them in response to these actions is available. Two approaches to constructing test sequences that guarantee the widest variety of situations arising in the course of testing are suggested. The first approach gives rise to the so-called de Bruijn sequences. The second approach yields sequences covering all states or transitions in all finite automata with the number of states not exceeding a given constant. Both kinds of sequences are related to the combinatorial analysis of words in finite alphabets. Some methods for constructing such sequences are also discussed.


Operating System Artificial Intelligence Software Engineer Test Sequence Minimum Information 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Hartman, A., Software and Hardware Testing Using Combinatorial Covering Suites. Haifa Workshop on Interdisciplinary Applications and Graph Theory, Combinatorics and Algorithms, June 2002, Scholar
  2. 2.
    Hartman, A. and Raskin, L., Problems and Algorithms for Covering Arrays, Discrete Math., 2004, vol. 284, pp. 149–156, Scholar
  3. 3.
    Colbourn, C.J., Combinatorial Aspects of Covering Arrays, Proc. of Combinatorics 2004, Capomulini, Italy, September 2004, Scholar
  4. 4.
    Fredricksen, H. and Maiorana, J., The Baltimore Hilton Problem, Technol. Rev., June 1980, vol. 83, no.7.Google Scholar
  5. 5.
    Marie, F.-S., Solution to Problem Number 58, L'Inermediaire des Mathematiciens, 1894, vol. 1, pp. 107–110.Google Scholar
  6. 6.
    De Bruijn, N.G., A Combinatorial Problem, Koninklijke Nederlandse Akademie van Wetenschappen, 1946, vol. 49, pp. 758–764.MATHGoogle Scholar
  7. 7.
    Martin, M.H., A Problem in Arrangements, Bull. Am. Math. Soc., 1934, no. 40, pp. 859–864.Google Scholar
  8. 8.
    Good, I.J., Normally Recurring Decimals, J. London Math. Soc., 1946, vol. 21, pp. 167–169.MathSciNetMATHGoogle Scholar
  9. 9.
    Rees, D., Note on a Paper by I.J. Good, J. London Math. Soc., 1946, vol. 21, pp. 169–172.MathSciNetMATHGoogle Scholar
  10. 10.
    Knuth, D.E., The Art of Computer Programming, vol. 1: Fundamental Algorithms, Reading: Addison-Wesley, 1968. Translated under the title Iskusstvo programmirovaniya, tom 1: Osnovnye algoritmy, Moscow: Vil'yams, 2002.Google Scholar
  11. 11.
    Fredricksen, H., A Survey of Full Length Nonlinear Shift Register Cycle Algorithm, SIAM Rev., 1982, vol. 24, no.2, pp. 195–221.CrossRefMathSciNetMATHGoogle Scholar
  12. 12.
    MacWilliams, F.J. and Sloane N.J.A., Pseudo-Random Sequences and Arrays, Proc. IEEE, 1976, vol. 64, pp. 1715–1729.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Savage, C.D., A Survey of Combinatorial Gray Codes, SIAM Rev., 1997, vol. 39, no.4, pp. 605–629.CrossRefMathSciNetMATHGoogle Scholar
  14. 14.
    Fan Chung and Cooper, J.N., De Bruijn Cycles for Covering Codes, 2003, Scholar
  15. 15.
    Zhang, L., Curless, B., and Seitz, S.M., Rapid Shape Acquisition Using Color Structured Light and Multi-Pass Dynamic Programming, Int. Symp. on 3D Data Processing Visualization and Transmission, Padova, Italy, June 2002, pp. 24–36.Google Scholar
  16. 16.
    Pages, J. and Salvi, J., A New Optimized De Bruijn Coding Strategy for Structured Light Patterns, 17th Int. Conf. on Pattern Recognition ICPR 2004, Cambridge, UK, 23–26 August, 2004.Google Scholar
  17. 17.
    Golomb, S.W., Shift Register Sequences, Laguna Hills: Aegean Park, 1981.Google Scholar
  18. 18.
    Lempel, A., On a Homomorphism of the de Bruijn Graph and its Applications to the Design of Feedback Shift Registers, IEEE Trans. Comput., 1970, vol. 19, pp. 1204–1209.MathSciNetMATHGoogle Scholar
  19. 19.
    Robinson, H., Graph Theory Techniques in Model-Based Testing, 1999 Int. Conf. on Testing Comput. Software, 1999, Scholar
  20. 20.
    Fredricksen, H. and Maiorana, J., Necklaces of Beads in k Colors and k-ary de Bruijn Sequences, Discrete Math., 1978, vol. 23, pp. 207–210.MathSciNetMATHGoogle Scholar
  21. 21.
    Etzion, T. and Lempel, A., Algorithms for the Generation of Full-Length Shift-Register Sequences, IEEE Trans. Information Theory, 1984, vol. 30, pp. 480–484.MathSciNetMATHGoogle Scholar
  22. 22.
    Etzion, T., An Algorithm for Constructing m-ary de Bruijn Sequences, J. Algorithms, 1986, vol. 7, pp. 331–340.CrossRefMathSciNetMATHGoogle Scholar
  23. 23.
    Games, R.A., A Generalized Recursive Construction for de Bruijn Sequences, IEEE Trans. Information Theory, 1983, vol. 29, pp. 843–850.MathSciNetMATHGoogle Scholar
  24. 24.
    Jansen, C.J.A., Franx, W.G., and Boekee, D.E., An Efficient Algorithm for the Generation of de Bruijn Cycles, IEEE Trans. Information Theory, 1991, vol. 37, pp. 1475–1478.CrossRefMathSciNetMATHGoogle Scholar
  25. 25.
    Ralston, A., A New Memoryless Algorithm for de Bruijn Sequences, J. Algorithms, 1981, vol. 2, pp. 50–62.CrossRefMathSciNetMATHGoogle Scholar
  26. 26.
    Roth, E., Permutations Arranged around a Circle, The Am. Math. Monthly, 1971, vol. 78, pp. 990–992.MathSciNetMATHGoogle Scholar
  27. 27.
    Xie, S., Notes on de Bruijn Sequences, Discrete Math., 1987, vol. 16, pp. 157–177.MATHGoogle Scholar
  28. 28.
    Annexstein, F.S., Generating de Bruijn Sequences: An Efficient Implementation, IEEE Trans. Comput., 1997, vol. 46, no.2, pp. 198–200.CrossRefGoogle Scholar
  29. 29.
    Vassallo, M. and Ralston, A., Algorithms for de Bruijn Sequences—a Case Study in the Empirical Analysis of Algorithms, The Comput. J., 1992, vol. 35, pp. 88–90.Google Scholar
  30. 30.
    O'Brien, M.J., De Bruijn Graphs and the Ehrenfeucht-Mycielski Sequence, Master's Thesis, Mathematical Science Department, Carnegie Mellon University, 2001.Google Scholar
  31. 31.
    Ivanyi, A., On the d-Complexity of Words, Ann. Univ. Sci. Budapest. Sect. Comput., 1987, no. 8, pp. 69–90.Google Scholar
  32. 32.
    Flaxman, A., Harrow, A.W., and Sorkin, G.B., Strings with Maximally Many Distinct Subsequences and Substrings, Electronic J. Combinatorics, 2004, vol. 11, no.1, Scholar
  33. 33.
    Aleliunas, R., Karp. R.M., Lipton, R.J., Lovasz, L., and Rackoff, C.W., Random Walks, Universal Traversal Sequences, and the Complexity of Maze Problems, Proc. of 20th Ann. Symp. on Foundations of Computer Sci, San Juan, Puerto Rico, October 1979, pp. 218–223.Google Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2005

Authors and Affiliations

  • V. V. Kuliamin
    • 1
  1. 1.Institute for System ProgrammingRussian Academy of SciencesMoscowRussia

Personalised recommendations