Expected Reachability-Time Games

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 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-NE...

• Type: Journal
• Year: 2010
• Where: FORMATS
• Authors: Vojtech Forejt, Marta Z. Kwiatkowska, Gethin Norman, Ashutosh Trivedi
• Keywords: Concurrent Ertgs, Formal Methods, FORMATS 2010, Game, Turn-based Ertgs