Expected reachability-time games

  • Authors:

  • Vojtěch Forejt;Marta Kwiatkowska;Gethin Norman;Ashutosh Trivedi

  • Affiliations:

  • Faculty of Informatics, Masaryk University, Brno, Czech Republic;Oxford University Computing Laboratory, Oxford, UK;Department of Computing Science, University of Glasgow, Glasgow, UK;Oxford University Computing Laboratory, Oxford, UK

  • Venue:
  • FORMATS'10 Proceedings of the 8th international conference on Formal modeling and analysis of timed systems
  • Year:
  • 2010

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Abstract

In an expected reachability-time game (ERTG) two players, Min and Max, move a token along the transitions of a probabilistic timed automaton, so as to minimise and maximise, respectively, the expected time to reach a target. These games are concurrent since at each step of the game both players choose a timed move (a time delay and action under their control), and the transition of the game is determined by the timed move of the player who proposes the shorter delay. A game is turn-based if at any step of the game, all available actions are under the control of precisely one player. We show that while concurrent ERTGs are not always determined, turn-based ERTGs are positionally determined. Using the boundary region graph abstraction, and a generalisation of Asarin and Maler's simple function, we show that the decision problems related to computing the upper/lower values of concurrent ERTGs, and computing the value of turn-based ERTGs are decidable and their complexity is in NEXPTIME ∩ co-NEXPTIME.