Question/Answer Games on Towers and Pyramids

  • Authors:

  • Sarmad Abbasi;Numan Sheikh

  • Affiliations:

  • , DHA, Pakistan 117-BB;Department of Computer Science, Lahore University of Management Sciences, DHA, Pakistan

  • Venue:
  • MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
  • Year:
  • 2008

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Abstract

Question/Answer games [3] (Q/A games) are a generalization of the game introduced in [1,2]. They are motivated by the classical game of twenty questions and are a generalization of Rényi-Ulam Game. A k-round Q/A game, G= (D,(q1, ..., qk)), is played on a rooted directed acyclic graph, D= (V,E). In the i-th round, Paul selects a set, Qi茂戮驴 V, of at most qinon-terminal vertices. Carole responds by choosing an outgoing edge from each vertex in Qi. At the end of krounds, Paul wins if Carole's answers define a unique path from the root to one of the terminal vertices in D. Arbitrary Q/A games are known to be PSPACE-complete [3], and k-round games are known to be Σ2k茂戮驴 2-complete [4]. In this paper we study Q/A games on two classes of graphs, towers and pyramids, respectively. We completely solve the problem of determining the winner for Q/A games on towers. We also solve an open problem on Q/A games on pyramids from [1,2]. Furthermore, we give some non-trivial lower and upper bounds for the rest of the cases for Q/A games on pyramids.