关键词：多项式时间；MDP；PCTL；共织协议
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 rst 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 veri cation algorithm for CMDPs, and prove that it runs in time polynomial in the size of a CMDP for a rich subclass of convex uncertainty models. This result allows us to lower the previously known algorithmic complexity upper bound for IMDPs from co-NP to PTIME. Using the proposed approach, we verify a consensus protocol and a dynamic con guration protocol for IPv4 addresses.