How Much Lookahead is Needed to Win Infinite Games?

  • Felix Klein
  • Martin Zimmermann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9135)


Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent’s moves. For \(\omega \)-regular winning conditions it is known that such games can be solved in doubly-exponential time and that doubly-exponential lookahead is sufficient.

We improve upon both results by giving an exponential time algorithm and an exponential upper bound on the necessary lookahead. This is complemented by showing \(\textsc {ExpTime}\)-hardness of the solution problem and tight exponential lower bounds on the lookahead. Both lower bounds already hold for safety conditions. Furthermore, solving delay games with reachability conditions is shown to be \(\textsc {PSpace}\)-complete.


Safety Condition Winning Strategy Reachability Condition Delay Function Tree Transducer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Reactive Systems GroupSaarland UniversitySaarbrückenGermany

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