Skip to main content
SpringerLink
Log in
Book cover

International Computing and Combinatorics Conference

COCOON 1996: Computing and Combinatorics pp 50–55Cite as

Finding a hidden code by asking questions

  • Session 2
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1090))

Abstract

We study the problem of finding a hidden code k in the domain {1, ..., m}n in the presence of an oracle which, for any x in the domain, answers a pair of numbers a(x,k) and b(x,k) such that a(x,k) is the number of components coinciding in x and k and, b(x, k) is the sum of a(x, k) and the number of components occurring in both x and k but, not at the same position. We show that \(\left\lceil {\frac{m}{n}} \right\rceil\)+ 2nlogn + 2n + 2 queries are sufficient to find any hidden code if m ≥ n.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D. Angluin, “Queries and concept learning”, Machine Learning, 2, pages 319–342, 1988.

    Google Scholar 

  2. A. Alon, J. Bruck, J. Naor, M. Naor, R. Roth, “Construction of asymptotically good low rate error-correcting codes through pseudo-random graphs”, IEEE Transactions on Information Theory, 38, pages 509–516, 1992.

    Google Scholar 

  3. V. Chvátal, Mastermind, Combinatorica, 3, pages 325–329, 1983.

    Google Scholar 

  4. M. Flood, Mastermind Strategy, J. of Recreational Mathematics, 18, pages 194–202, 1985–86.

    Google Scholar 

  5. D.E. Knuth, The computer as Mastermind, J. of Recreational Mathematics, 9, pages 1–6, 1976–77.

    Google Scholar 

  6. R.W. Irving, “Towards an optimum Mastermind strategy”, J. of Recreational Mathematics, 11, pages 81–87, 1978–79.

    Google Scholar 

  7. E. Neuwirth, Some strategies for Mastermind, Zeitschrift für Operations Research, 26, pages 257–278, 1982.

    Google Scholar 

  8. G. Seroussi, N. Bshouty, “Vector sets for exhaustive testing of logic circuits”, IEEE Transactions on Information Theory, 34, pages 513–522, 1988.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Math and Computer Science, Southwest State University, 56258, Marshall, MN, USA

    Zhixiang Chen

  2. Dept. of Computer Science, Boston University, 02215, Boston, MA, USA

    Carlos Cunha & Steven Homer

Authors
  1. Zhixiang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carlos Cunha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Steven Homer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jin-Yi Cai Chak Kuen Wong

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, Z., Cunha, C., Homer, S. (1996). Finding a hidden code by asking questions. In: Cai, JY., Wong, C.K. (eds) Computing and Combinatorics. COCOON 1996. Lecture Notes in Computer Science, vol 1090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61332-3_138

Download citation

  • DOI: https://doi.org/10.1007/3-540-61332-3_138

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61332-9

  • Online ISBN: 978-3-540-68461-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation