Solving infinite games on trees with back-edges

  • Authors:
  • Aniruddh Gandhi;Bakhadyr Khoussainov;Jiamou Liu

  • Affiliations:
  • University of Auckland, Auckland, New Zealand;University of Auckland, Auckland, New Zealand;Auckland University of Technology, Auckland, New Zealand

  • Venue:
  • CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
  • Year:
  • 2012

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Abstract

We study the computational complexity of solving the following problem: Given a game g played on a finite directed graph G, output all nodes in G from which a specific player wins the game g. We provide algorithms for solving the above problem when the games have Büchi and parity winning conditions and the graph G is a tree with back-edges. The running time of the algorithm for Büchi games is O(min{r·m, l + m}) where m is the number of edges, l is the sum of the distances from the root to all leaves and the parameter r is bounded by the height of the tree. The algorithm for parity has a running time of O(l + m).