Optimal Strategy Synthesis in Request-Response Games

  • Authors:

  • Florian Horn;Wolfgang Thomas;Nico Wallmeier

  • Affiliations:

  • LIAFA, Université Paris 7, Paris 5, France F-75251 and Lehrstuhl für Informatik 7, RWTH Aachen University, Aachen, Germany 52056;Lehrstuhl für Informatik 7, RWTH Aachen University, Aachen, Germany 52056;Lehrstuhl für Informatik 7, RWTH Aachen University, Aachen, Germany 52056

  • Venue:
  • ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
  • Year:
  • 2008

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Abstract

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 Qis visited, then later a state with property Pis 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.