Optimal Strategy Synthesis in Request-Response Games

  • Florian Horn
  • Wolfgang Thomas
  • Nico Wallmeier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5311)


We show the solvability of an optimization problem on infinite two-player games. The winning conditions are of the “request-response” format, i.e. conjunctions of conditions of the form “if a state with property Q is visited, then later a state with property P is visited”. We ask for solutions that do not only guarantee the satisfaction of such conditions but also minimal wait times between visits to Q-states and subsequent visits to P-states. We present a natural class of valuations of infinite plays that captures this optimization problem, and with respect to this measure show the existence of an optimal winning strategy (if a winning strategy exists at all) and that it can be realized by a finite-state machine. For the latter claim we use a reduction to the solution of mean-payoff games due to Paterson and Zwick.


Wait Time Temporal Logic Memory State Path Segment Linear Time Temporal Logic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Florian Horn
    • 1
    • 2
  • Wolfgang Thomas
    • 2
  • Nico Wallmeier
    • 2
  1. 1.LIAFAUniversité Paris 7Paris 5France
  2. 2.Lehrstuhl für Informatik 7RWTH Aachen UniversityAachenGermany

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