The Complexity of Request-Response Games

  • Krishnendu Chatterjee
  • Thomas A. Henzinger
  • Florian Horn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6638)


We consider two-player graph games whose objectives are request-response condition, i.e conjunctions of conditions of the form “if a state with property Rq is visited, then later a state with property Rp is visited”. The winner of such games can be decided in EXPTIME and the problem is known to be NP-hard. In this paper, we close this gap by showing that this problem is, in fact, EXPTIME-complete. We show that the problem becomes PSPACE-complete if we only consider games played on DAGs, and NP-complete or PTIME-complete if there is only one player (depending on whether he wants to enforce or spoil the request-response condition).

We also present near-optimal bounds on the memory needed to design winning strategies for each player, in each case.


Memory State Winning Strategy Linear Time Temporal Logic Winning Region Opposing Player 
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 2011

Authors and Affiliations

  • Krishnendu Chatterjee
    • 1
  • Thomas A. Henzinger
    • 1
  • Florian Horn
    • 1
    • 2
  1. 1.IST (Institute of Science and Technology)Austria
  2. 2.LIAFA, CNRS & UniversitéParis 7France

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