The complexity of synchronizing Markov decision processes

摘要

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 consider four temporal synchronizing modes: a sequence of probability distributions is always p-synchronizing, eventually p-synchronizing, weakly p-synchronizing, or strongly p-synchronizing if, respectively, all, some, infinitely many, or all but finitely many distributions in the sequence are p-synchronizing. We provide tight results on the expressiveness, decidability, complexity, and memory requirement for winning strategies for all synchronizing modes in MDPs.