"Duality, approximations and distances for probabilistic processes"

该研究项目的总体目标是建立对并发概率过程进行推理的形式化方法。特别是，我对具有连续状态空间的过程感兴趣，但在离散时间步长中被观察到：这些系统的一个众所周知的模型被标记为马尔可夫过程（LMPs）。**可能的应用领域包括通信协议和过程控制软件。对于这样的系统，我们想要对正确性、性能和安全关键属性进行推理。****我想从理论和实践两个方面来发展这个领域。我与lmp一起工作，但也与lmp一起工作，这是lmp的推广，其中通常要求度量是相加的。该模型包含了常见的模型：概率转移系统、lmp、概率自动机。它允许对未指定的系统建模，例如我们只有不完整规范的系统。************

The general goal of the research project is to establish formal methods for reasoning about concurrent probabilistic processes. In particular, I am interested in processes that have a continuous state-space, but are observed in discrete time steps: a well-known model for these systems are Labelled Markov Processes (LMPs).**Possible application areas include communication protocols and process control software. For such systems we would like to reason about correctness, performance and safety critical properties.****I want to develop the field along theoretic and practical sides. I work with LMPs, but also with infLMPs, which are a generalisation of LMPs where the usual requirement for measures to be additive is dropped. This model subsumes the usual ones: probabilistic transition systems, LMPs, probabilistic automata. It allows to model underspecified systems, for example systems for which we only have incomplete specification. ************