This article presents the complexity of reachability decision problems for parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters. In particular, we study the complexity of finding values for these parameters such that the induced MDP satisfies some maximal or minimal reachability probability constraints. We discuss different variants depending on the comparison operator in the constraints and the domain of the parameter values. We improve all known lower bounds for this problem, and notably provide ETR-completeness results for distinct variants of this problem.

本文介绍了参数化马尔可夫决策过程（pMDP）的可达性决策问题的复杂性，这是对马尔可夫决策过程（MDP）的扩展，其中通过概率对一组有限的参数进行多项式描述了转移概率。特别是，我们研究了找到这些参数的值的复杂性，以使诱导的MDP满足某些最大或最小可达性概率约束。我们根据约束条件和参数值域中的比较运算符来讨论不同的变体。我们改善了此问题的所有已知下限，并特别提供了此问题的不同变体的ETR完整性结果。