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[FKNT10a] V. Forejt, M. Kwiatkowska, G. Norman and A. Trivedi. Expected Reachability-Time Games. In K. Chatterjee and T. Henzinger (editors), Proeedings of 8th International Conference on Formal Modelling and Analysis of Timed Systems (FORMATS'10), volume 6246 of LNCS, pages 122--136, Springer. September 2010. [pdf] [bib]
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Notes: See [FKNT16] for a journal version of the paper, with full proofs and several error fixes. An technical report for this conference paper can be found in [FKNT10b]. The original publication is available at link.springer.com.
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.