Degrees of Lookahead in Regular Infinite Games

  • Michael Holtmann
  • Łukasz Kaiser
  • Wolfgang Thomas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6014)


We study variants of regular infinite games where the strict alternation of moves between the two players is subject to modifications. The second player may postpone a move for a finite number of steps, or, in other words, exploit in his strategy some lookahead on the moves of the opponent. This captures situations in distributed systems, e.g. when buffers are present in communication or when signal transmission between components is deferred. We distinguish strategies with different degrees of lookahead, among them being the continuous and the bounded lookahead strategies. In the first case the lookahead is of finite possibly unbounded size, whereas in the second case it is of bounded size. We show that for regular infinite games the solvability by continuous strategies is decidable, and that a continuous strategy can always be reduced to one of bounded lookahead. Moreover, this lookahead is at most doubly exponential in the size of the parity automaton recognizing the winning condition. We also show that the result fails for non-regular games where the winning condition is given by a context-free ω-language.


Continuous Operator Winning Strategy Delay Operator Constant Delay Game Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Michael Holtmann
    • 1
  • Łukasz Kaiser
    • 2
  • Wolfgang Thomas
    • 1
  1. 1.RWTH Aachen, Lehrstuhl für Informatik 7Aachen
  2. 2.RWTH Aachen, Mathematische Grundlagen der InformatikAachen

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