## Expected Reachability-time Games.

Vojtech Forejt, Marta Kwiatkowska, Gethin Norman, and Ashutosh Trivedi

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 $$\cap$$ co-NEXPTIME.

Proceedings of the th International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS 09), Lecture Notes in Computer Science Volume 6246, 2010, pp 122-136, Springer.
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