Q-ary search with one lie and bi-interval queries

  • Authors:

  • Wen An Liu;Kun Meng;Shu Min Xing

  • Affiliations:

  • College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, People's Republic of China;College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, People's Republic of China;College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, People's Republic of China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2007

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Abstract

The following search game is considered: there are two players, say Paul (or questioner) and Carole (or responder). Carole chooses a number x^*@?S"n={1,2,...,n}, Paul has to find the number x^* by asking q-ary bi-interval queries and Carole is allowed to lie at most once throughout the game. The minimum worst-case number L"B(n,q,1) of q-ary bi-interval queries necessary to guess the number x^* is determined exactly for all integers n=1 and q=2. It turns out that L"B(n,q,1) coincides with the minimum worst-case number L(n,q,1) of arbitrary q-ary queries.