关键词：运行时验证；概率计算树逻辑；马尔可夫决策过程；PCTL；凸锥；多项式
摘 要：We address the problem of verifying Probabilistic Computation Tree Logic (PCTL) properties of Markov Decision Processes (MDPs) whose state transition probabilities are only known to lie within uncertainty sets.We first introduce the model of Convex-MDPs (CMDPs), i.e., MDPs with convex uncertainty sets. CMDPs generalize Interval-MDPs (IMDPs) by allowing also more expressive (convex) descriptions of uncertainty.Using results on strong duality for convex programs, we then present a PCTL verification algorithm for CMDPs, and prove that it runs in time polynomial in the size of a CMDP. This result allows us to lower the previously known algorithmic complexity upper bound for IMDPs from co-NP to PTIME, and it is valid also for more expressive (convex) uncertainty models.We validate the proposed approach on two case studies: the verification of a consensus protocol and of a dynamic configuration protocol for IPv4 addresses.