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Without loss of generality, we may assume that V g consists of a single goal state g such that no edge exits from g; the reduction to this special case is obvious. There is a probability function p mapping edges exiting from passive nodes to positive real numbers such that, for every u ∈ V p , p(u, v) = 1. (1) (u,v)∈E Notice that this implies that for every passive state there is at least one edge starting from it, and we assume the same for active states. Finally, there is a cost function c from edges to positive real numbers.
In Section 2, reachability games are formulated, analysed and solved by means of linear programming and various known results, in particular [10, Theorem 9]. We associate a state dependent cost with each action. The optimal strategy minimizes the expected total cost which is the sum of the costs incurred during the execution. We observe that a reachability game can be viewed as a negative Markov decision process with infinite horizon ; the stopping condition is the first arrival at a final state.
Otherwise, the test model would allow executing first one keyword in one application and then another keyword in another application without activating the other application first. This would lead to a situation where the test model assumes that both applications have received one input, but in reality, the first application received two inputs and the other none. Because the activation itself must be expressed as a sequence of keywords, it is natural to model the task switcher as a special application, a sort of a scheduler.