The Interval Liar Game

  • Benjamin Doerr
  • Johannes Lengler
  • David Steurer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


We regard the problem of communication in the presence of faulty transmissions. In contrast to the classical works in this area, we assume some structure on the times when the faults occur. More realistic seems the “burst error model”, in which all faults occur in some small time interval.

Like previous work, our problem can best be modelled as a two-player perfect information game, in which one player (“Paul”) has to guess a number x from {1, ..., n} using Yes/No-questions, which the second player (“Carole”) has to answer truthfully apart from few lies. In our setting, all lies have to be in a consecutive set of k rounds.

We show that (for big n) Paul needs roughly logn+loglogn+k rounds to determine the number, which is only k more than the case of just one single lie.


Winning Strategy Formal Choice Consecutive State Game Position Triangle Equality 
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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  1. [BK93]
    Borgstrom, R.S., Kosaraju, S.R.: Comparison-based search in the presence of errors. In: STOC, pp. 130–136 (1993)Google Scholar
  2. [CM99]
    Cicalese, F., Mundici, D.: Optimal binary search with two unreliable tests and minimum adaptiveness. In: Nešetřil, J. (ed.) ESA 1999. LNCS, vol. 1643, pp. 257–266. Springer, Heidelberg (1999)Google Scholar
  3. [Pel87]
    Pelc, A.: Solution of Ulam’s problem on searching with a lie. J. Comb. Theory, Ser. A 44(1), 129–140 (1987)MATHCrossRefMathSciNetGoogle Scholar
  4. [Pel89]
    Pelc, A.: Searching with known error probability. Theor. Comput. Sci. 63(2), 185–202 (1989)MATHCrossRefMathSciNetGoogle Scholar
  5. [Pel02]
    Pelc, A.: Searching games with errors - fifty years of coping with liars. Theor. Comput. Sci. 270(1-2), 71–109 (2002)MATHCrossRefMathSciNetGoogle Scholar
  6. [Rén61]
    Rényi, A.: On a problem of information theory. MTA Mat. Kut. Int. Kozl. 6B, 505–516 (1961)Google Scholar
  7. [Rén76]
    Rényi, A.: Napl’o az információelméletről, Gondolat, Budapest (1976), (English translation: A Diary on Information Theory, Wiley, New York, 1984) Google Scholar
  8. [Spe92]
    Spencer, J.: Ulam’s searching game with a fixed number of lies. Theor. Comput. Sci. 95(2), 307–321 (1992)MATHCrossRefGoogle Scholar
  9. [Ula76]
    Ulam, S.M.: Adventures of a Mathematician, p. 281. Scribner, New York (1976)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Benjamin Doerr
    • 1
  • Johannes Lengler
    • 2
  • David Steurer
    • 3
  1. 1.Max–Planck–Institut für InformatikSaarbrückenGermany
  2. 2.Mathematics DepartmentSaarland UniversitySaarbrücken
  3. 3.Computer Science DepartmentPrinceton UniversityPrinceton

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