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The Multi-interval Ulam-Rényi Game

  • Ferdinando Cicalese
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7288)

Abstract

We try to help Paul and Pinocchio to deserve their trip to Venice where they are planning to continue a 50-year long competition in the 20 question game with lies.

Keywords

Search Space Binary Search Large Pack Discrete Apply Mathematic Binary Symmetric Channel 
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.

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References

  1. 1.
    Ahlswede, R., Cicalese, F., Deppe, C., Vaccaro, U.: Two Batch Search with Lie Cost. IEEE Transaction on Information Theory 55(4), 1433–1439 (2009)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Aslam, J., Dhagat, A.: Searching in the presence of linearly bounded errors. In: Proc. of 23rd STOC, pp. 486–493 (1991)Google Scholar
  3. 3.
    Berlekamp, E.R.: Block coding for the binary symmetric channel with noiseless, delayless feedback. In: Mann, H.B. (ed.) Error-Correcting Codes, pp. 61–68. Wiley, New York (1968)Google Scholar
  4. 4.
    Cicalese, F., Mundici, D.: Perfect 2-fault tolerant search with minimum adaptiveness. Advances in Applied Mathemathics 25, 65–101 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Cicalese, F., Mundici, D., Vaccaro, U.: Rota-Metropolis cubic logic and Ulam-Rényi games. In: Crapo, H., Senato, D. (eds.) Algebraic Combinatorics and Computer Science—A Tribute to Giancarlo Rota, pp. 197–244. Springer Italia (2001)Google Scholar
  6. 6.
    Cicalese, F., Mundici, D., Vaccaro, U.: Least Adaptive Optimal Search with Unreliable Tests. Theoretical Computer Science 270(1-2), 877–893 (2001)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cicalese, F., Deppe, C.: Quasi-Perfect Minimally Adaptive q-ary Search with Unreliable Tests. In: Ibaraki, T., Katoh, N., Ono, H. (eds.) ISAAC 2003. LNCS, vol. 2906, pp. 527–536. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Cicalese, F., Gargano, L., Vaccaro, U.: On searching strategies, parallel questions, and delayed answers. Discrete Applied Mathematics 144, 247–262 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Cicalese, F., Mundici, D.: Recent Developments of Feedback Coding and Its Relations with Many-Valued Logic. In: van Benthem, J., et al. (eds.) Proof, Computation and Agency, vol. 352(3), pp. 115–131. Springer–Verlag Synthese Library (2011)Google Scholar
  10. 10.
    Deppe, C.: Coding with feedback and searching with lies. In: Entropy, Search, Complexity. Bolyai Society Mathematical Studies, vol. 16, pp. 27–70 (2007)Google Scholar
  11. 11.
    Dhagat, A., G’acs, P., Winkler, P.: On Playing “Twenty Questions” with a liar. In: Proc. of 3rd SODA, pp. 16–22 (1992)Google Scholar
  12. 12.
    Mundici, D., Trombetta, A.: Optimal comparison strategies in Ulam’s searching game with two errors. Theoretical Computer Science 182, 217–232 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Pedrotti, A.: Playing by searching: two strategies against a linearly bounded liar. Theoretical Computer Science 282, 285–302 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Pelc, A.: Searching games with errors—Fifty years of coping with liars. Theoretical Computer Science 270(1-2), 71–109 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Pelc, A.: Coding with bounded error fraction. Ars. Combinat. 24, 17–22 (1987)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Rényi, A.: On a problem of information theory. MTA Mat. Kut. Int. Kozl. 6B, 505–516 (1961)Google Scholar
  17. 17.
    Rivest, R.L., Meyer, A.R., Kleitman, D.J., Winklmann, K., Spencer, J.: Coping with errors in binary search procedures. JCSS 20, 396–404 (1980)zbMATHGoogle Scholar
  18. 18.
    Sereno, M.: Binary search with errors and variable cost queries. Information Processing Letters 68(5), 261–270 (1998)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Spencer, J., Winkler, P.: Three thresholds for a liar. Combinatorics, Probability and Computing 1, 81–93 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Spencer, J.: Guess a number with Lying. Math. Magazine 57, 105–108 (1984)zbMATHCrossRefGoogle Scholar
  21. 21.
    Spencer, J.: Ulam’s searching game with a fixed number of lies. Theoretical Computer Science 95, 307–321 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Ulam, S.M.: Adventures of a Mathematician. Scribner’s, New York (1976)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ferdinando Cicalese
    • 1
  1. 1.Department of Computer ScienceUniversity of SalernoItaly

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