Skip to main content
SpringerLink
Log in

The Russian Cards Problem

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

Suppose we have a stack of cards that is divided over some players. For certain distributions of cards it is possible to communicate your hand of cards to another player by public announcements, without yet another player learning any of your cards. A solution to this problem consists of some sequence of announcements and is called an exchange. It is called a direct exchange if it consists of (the minimum of) two announcements only. The announcements in an exchange have a special form: they are safe communications, an interesting new form of update. Certain unsafe communications turn out to be unsuccessful updates. A communication is a public announcement that is known to be true. Each communication may be about a set of alternative card deals only, and even about a set of alternatives to the communicating player's own hand only. We list the direct exchanges for a deal of seven cards where the two players holding three cards communicate their hands to each other. Our work may be applicable to the design of cryptographic protocols.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Agray, N., W. Van Der Hoek, and E. De Vink, ‘On ban logics for industrial security protocols’, in B. Dunin-Keplicz and E. Nawarecki, (eds.), From Theory to Practice in Multi-Agent Systems, pp. 29-38. LNAI 2296, Springer, Berlin, 2002.

    Google Scholar 

  2. Baltag, A., ‘A logic for suspicious players: Epistemic actions and belief updates in games’, Bulletin of Economic Research, 54(1):1-45, 2002.

    Google Scholar 

  3. Burrows, M., M. Abadi, and R. Needham, ‘A logic of authentication’, ACM Transactions on Computer Systems, 8:18-36, 1990.

    Google Scholar 

  4. Engelhardt, K., R. Van Der Meyden, and Y. Moses, ‘Knowledge and the logic of local propositions’, in I. Gilboa, (ed.), Proceedings of TARK VII, pp. 29-41. Morgan Kaufmann, Los Altos, 1998.

    Google Scholar 

  5. Fagin, R., J. Y. Halpern, Y. Moses, and M. Y. Vardi, Reasoning about Knowledge, MIT Press, Cambridge MA, 1995.

    Google Scholar 

  6. Fischer, M. J., and R. N. Wright, ‘Bounds on secret key exchange using a random deal of cards’, Journal of Cryptology, 9(2):71-99, 1996.

    Google Scholar 

  7. Gerbrandy, J. D., Bisimulations on Planet Kripke, PhD thesis, University of Amsterdam, 1999. ILLC Dissertation Series DS-1999-01.

  8. Gerbrandy, J. D., and W. Groeneveld, ‘Reasoning about information change’, Journal of Logic, Language, and Information, 6:147-169, 1997.

    Google Scholar 

  9. Graham, R. L., M. Grotschel, and L. Lovasz, (eds.), Handbook of Combinatorics, MIT Press, Cambridge MA, 1996.

    Google Scholar 

  10. Makarychev, K., Logicheskie voprosy peredachi informacii (logical issues of information transmission), Master's thesis, Moscow State University, 2001. Diplomnaja rabota, part 1.

  11. Makarychev, K. S., and Yu. S. Makarychev, ‘The importance of being formal’, Mathematical Intelligencer, 23(1):41-42, 2001.

    Google Scholar 

  12. Meyer, J.-J. Ch., and W. Van Der Hoek, Epistemic Logic for AI and Computer Science. Cambridge Tracts in Theoretical Computer Science 41, Cambridge University Press, Cambridge, 1995.

    Google Scholar 

  13. Plaza, J. A., ‘Logics of public communications’, in M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, and Z. W. Ras, (eds.), Proceedings of the 4th International Symposium on Methodologies for Intelligent Systems, pp. 201-216, 1989.

  14. Stulp, F., and L. C. Verbrugge, ‘A knowledge-based algorithm for the internet transmission control protocol (tcp)’, Bulletin of Economic Research, 54(1):69-94, 2002.

    Google Scholar 

  15. Van Benthem, J. F. A. K., ‘Logics for information update’, in J. F. A. K. van Benthem, (ed.), Proceedings of TARK VIII, pp. 51-88, Morgan Kaufmann, Los Altos, 2001.

    Google Scholar 

  16. Van Benthem, J. F. A. K., P. Dekker, J. Van Eijck, M. De Rijke, and Y. Venema, Logic in Action, ILLC, Amsterdam, 2002.

    Google Scholar 

  17. Van Ditmarsch, H. P., Knowledge games, PhD thesis, University of Groningen, 2000. ILLC Dissertation Series DS-2000-06.

  18. Van Ditmarsch, H. P., ‘Killing cluedo’, Natuur & Techniek, 69(11):32-40, 2001.

    Google Scholar 

  19. Van Ditmarsch, H. P., ‘Knowledge games’, Bulletin of Economic Research, 53(4):249-273, 2001.

    Google Scholar 

  20. Van Ditmarsch, H. P., ‘Descriptions of game actions’, Journal of Logic, Language and Information, 11:349-365, 2002.

    Google Scholar 

  21. Van Ditmarsch, H. P., ‘Oplossing van het mysterie (solution of the murder mystery)’, Natuur & Techniek, 70(2):17, 2002.

    Google Scholar 

  22. Van Ditmarsch, H. P., W. Van Der Hoek, and B. P. Kooi, ‘Descriptions of game states’, in I. van Loon, G. Mints, and R. Muskens, (eds.), Proceedings of LLC9 (2000), CSLI Publications, Stanford. To appear.

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Otago, PO Box 56, 9015, Dunedin, New Zealand

    Hans van Ditmarsch

Authors
  1. Hans van Ditmarsch
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

van Ditmarsch, H. The Russian Cards Problem. Studia Logica 75, 31–62 (2003). https://doi.org/10.1023/A:1026168632319

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026168632319

Search

Navigation