Synthesis and Verification in Markov Game Structures

为了实现我们项目的目标，我们将把研究分为五个工作包。第一个工作包致力于描述我们想要解决的控制问题，并确定基准和案例研究，作为我们项目应用方面的相关需求和成功衡量标准的指南。我们的模型的出发点将是-将交互式马尔可夫链推广到2.5玩家游戏，在该模型中，不同玩家的决策通过将其分配到不同的状态而物理分离，以及-将马尔可夫决策过程推广到马尔可夫游戏，在该模型中，（或者，更一般地说，所有）参与者都纠缠在同一个节点上。我们将通过考虑控制器的观测和计算能力的表示来扩展这些模型，此外，我们将开发基准和案例研究，以指导我们项目的应用方面，并通过反映不同社区的需求，使其扎根于不同社区，特别是工程和IT领域。工作包二，三，四是我们工作的理论核心。我们的第二个工作包将解决构造具有完整信息的控制器的简单问题，而第三个工作包将解决这些技术到具有不完整信息的控制器的推广，但是对于分布式控制器，关于系统状态的等效信息。当考虑这些系统的不完全信息时，时间的抽象（或受限的可观测性）起着至关重要的作用。这种特殊类型的抽象已被证明经常简化最佳策略的构建：最优时间抽象策略的构造（以及它们存在的证明）比构造依赖于时间的要简单得多。第四个工作包是指将这些结果扩展到具有不同观测能力的分布式观测器。对于工作包二，三和四，我们将研究定量和定性安全性和可达性属性的可判定性。在第五个工作包中，我们将专注于算法方面，如模型检查和优化问题的适当数据结构的开发和选择，并开发原型实现，解决作为一个概念验证其适用性的选择开发的方法。这些概念验证实现还将在确定项目中开发的技术在第一个工作包中定义的目标实现上的适用性和潜力方面发挥重要作用，并作为传播和开发目的的结果的手段。

To meet the objectives of our project, we will divide our research into five work packages.The first work package is devoted to representing the control problems that we want to approach and to identify benchmarks and case studies as guidelines for relevant demands and measures of success for the applied aspects of our project. The starting point for our models will be- a generalisation of interactive Markov chains to 2.5 player games, a model in which the decisions of the different players are physically separated by assigning them to different states, and- a generalisation of Markov decision processes to Markov games, a model in which the decisions of both (or, more generally, of all) players are entangled and represented in the same node.We will extend these models by representations of the observational and computational power of the controllers under consideration, and formalisations of the--simple--objectives we want to meet.Additionally, we will develop benchmarks and case studies to guide the applied aspects of our project, and to root it in different communities--in particular in engineering and IT--by reflecting their respective demands.Work packages two, three, and four from the theoretic core of our work. Our second work package will address the simple question of constructing controllers with complete information, while a third work package will address the generalisation of these techniques to controllers with incomplete information but, for distributed controllers, equivalent information about the system state.Different to discrete systems, the abstraction (or restricted observability) of time plays a paramount role when considering incomplete information of these systems. This particular type of abstraction has proven to often simplify the construction of optimal strategies: The construction of optimal time-abstract strategies (and the proof of their existence) is much simpler than the construction of time dependent ones.The fourth work package refers to the extension of these results to distributed schedulers with different observational power.For work packages two, three, and four, we will study the decidability of quantitative and qualitative safety and reachability properties.In a fifth work package we will focus on algorithmic aspects like the development and selection of appropriate data structures of the model checking and optimisation problems, and develop prototype implementations that solve as a proof-of-concept for their applicability for a selection of the developed approaches. These proof-of-concept implementations will also play an important role in determining the applicability and potential of the techniques developed in the project on the target implementations defined in the first work package, and as means to communicate our results for dissemination and exploitation purposes.