Probabilistic bisimulation is a fundamental notion of process equivalence for probabilistic systems. Among others, it has important applications including formalizing the anonymity property of several communication protocols. There is a lot of work on verifying probabilistic bisimulation for finite systems. This is however not the case for parameterized systems, where the problem is in general undecidable. In this paper we provide a generic framework for reasoning about probabilistic bisimulation for parameterized systems. Our approach is in the spirit of software verification, wherein we encode proof rules for probabilistic bisimulation and use a decidable first-order theory to specify systems and candidate bisimulation relations, which can then be checked automatically against the proof rules. As a case study, we show that our framework is sufficiently expressive for proving the anonymity property of the parameterized dining cryptographers protocol and the parameterized grades protocol, when supplied with a candidate regular bisimulation relation. Both of these protocols hitherto could not be verified by existing automatic methods. Moreover, with the help of standard automata learning algorithms, we show that the candidate relations can be synthesized fully automatically, making the verification fully automated.

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参数化系统的概率互仿真（技术报告）

概率互模拟是概率系统过程等效的基本概念。其中，它具有重要的应用，包括形式化几种通信协议的匿名属性。在验证有限系统的概率互模拟方面有很多工作。然而，对于参数化系统而言，情况并非如此，其中问题通常是不可判定的。在本文中，我们提供了一个通用框架，用于推理参数化系统的概率互模拟。我们的方法本着软件验证的精神，其中我们为概率互模拟编码证明规则，并使用可判定的一阶理论来指定系统和候选互模拟关系，然后可以根据证明规则自动检查这些关系。作为案例研究，我们表明，当提供候选规则互模拟关系时，我们的框架足以证明参数化餐饮密码协议和参数化等级协议的匿名性。迄今为止，这两种协议都无法通过现有的自动方法进行验证。此外，在标准自动机学习算法的帮助下，我们表明候选关系可以完全自动合成，使验证完全自动化。