Abstract model repair for probabilistic systems

Given a Discrete Time Markov Chain M and a probabilistic temporal logic formula φ, where M violates φ, the problem of Model Repair is to obtain a new model M′, such that M′ satisfies φ. Additionally, the changes made to M in order to obtain M′ should be minimum with respect to all such M′. The state explosion problem makes the repair of large probabilistic systems almost infeasible. In this paper, we use the abstraction of Discrete Time Markov Chains in order to speed-up the process of model repair for temporal logic reachability properties. We present a framework based on abstraction and refinement, which reduces the state space of the probabilistic system to repair at the price of obtaining an approximate solution. A metric space is defined over the set of DTMCs, in order to measure the differences between the initial and the repaired models. For the repair, we introduce an algorithm and we discuss its important properties, such as soundness and complexity. As a proof of concept, we provide experimental results for probabilistic systems with diverse structures of state spaces, including the well-known Craps game, the IPv4 Zeroconf protocol, a message authentication protocol and the gambler's ruin model.