Probabilistic Causes in Markov Chains

The paper studies a probabilistic notion of causes in Markov chains that relies on the counterfactuality principle and probability-raising property. This is motivated by use for monitoring purposes where aim to detect faulty or undesired behaviours before they actually occur. A cause set finite executions system after which probability effect exceeds given threshold. We introduce multiple types costs capture consump-tion resources from different perspectives, study complexity computing cost-minimal causes.