Q-ary Rényi-Ulam pathological liar game with one lie

  • Authors:

  • Kun Meng;Chuang Lin;Wen An Liu;Yang Yang

  • Affiliations:

  • School of Information Engineering, University of Science and Technology Beijing, Beijing 100083, People's Republic of China and Department of Computer Science and Technology, Tsinghua University, ...;Department of Computer Science and Technology, Tsinghua University, Beijing 100084, People's Republic of China;College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, People's Republic of China;School of Information Engineering, University of Science and Technology Beijing, Beijing 100083, People's Republic of China

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2011

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Abstract

The m-round q-ary Renyi-Ulam pathological liar game withelies, referred to as the game [q,e,n;m]^*, is considered. Two players, say Paul and Carole, fix nonnegative integers m, n, q and e. In each round, Paul splits [n]@?{1,2,...,n} into q subsets, and Carole chooses one subset as her answer and assigns 1 lie to all elements except those in her answer. Paul wins, after m rounds, if there exists at least one element assigned with e or fewer lies. Let f^*(q,e,n) be the maximum value of m such that Paul can certainly win the game [q,e,n;m]^*. This paper gives the exact value of f^*(q,1,n) for n=q^q^-^1 and presents a tight bound on f^*(q,1,n) for n