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When modeling concurrent or cyber-physical systems, non-functional requirements such as time are important to consider. In order to improve the timing aspects of a model, it is necessary to have some notion of what it means for a process to be faster than another, which can guide the stepwise refinement of the model. To this end we study a faster-than relation for semi-Markov decision processes and compare it to standard notions for relating systems. We consider the compositional aspects of this relation, and show that the faster-than relation is not a precongruence with respect to parallel composition, hence giving rise to so-called parallel timing anomalies. We take the first steps toward understanding this problem by identifying decidable conditions sufficient to avoid parallel timing anomalies in the absence of non-determinism.
We consider Markov decision processes (MDP) as generators of sequences of probability distributions over states. A probability distribution is p-synchronizing if the probability mass is at least p in a single state, or in a given set of states. We co
Semi-Markov processes are Markovian processes in which the firing time of the transitions is modelled by probabilistic distributions over positive reals interpreted as the probability of firing a transition at a certain moment in time. In this paper
We propose a simple technique for verifying probabilistic models whose transition probabilities are parametric. The key is to replace parametric transitions by nondeterministic choices of extremal values. Analysing the resulting parameter-free model
We introduce synchronizing objectives for Markov decision processes (MDP). Intuitively, a synchronizing objective requires that eventually, at every step there is a state which concentrates almost all the probability mass. In particular, it implies t
We investigate the problem of monitoring partially observable systems with nondeterministic and probabilistic dynamics. In such systems, every state may be associated with a risk, e.g., the probability of an imminent crash. During runtime, we obtain