Model checking has advanced over the last decades to become an effective formal technique for verifying distributed and concurrent systems. As computers grew in memory and processing capacity, it became possible to exhaustively verify systems with billions of states, making it practical to model and verify real-world protocols and algorithms. However, writing a model is a manual task that potentially introduces defects which the model checker tool finds to fulfill the formal specification (e.g., an incorrect model that fulfills an incomplete specification). Furthermore, this kind of formal verification technique is limited by the well-known state-space explosion problem. This paper aims to provide a set of generic template models, appropriate for distributed round-based algorithms, to be used to focus modeling effort on algorithm-specific details. To mitigate state-space explosion, the paper proposes two reduction techniques, named partition symmetry reduction and message order reduction, that exploit symmetries in the state space to avoid expanding equivalent states. The reusable framework for verifying round-based algorithms and the two proposed reduction techniques provide the means for reducing by orders of magnitude the number of states required to analyze common distributed algorithms.

在过去的几十年中，模型检查已经发展成为一种有效的形式技术，用于验证分布式和并发系统。随着计算机内存和处理能力的增长，有可能彻底验证具有数十亿状态的系统，从而使建模和验证实际协议和算法变得切实可行。但是，编写模型是一项人工任务，可能会引入一些缺陷，模型检查工具会发现这些缺陷会满足正式规范的要求（例如，规格不完整的不正确模型）。此外，这种形式验证技术受到众所周知的状态空间爆炸问题的限制。本文旨在提供一组适用于基于分布式回合算法的通用模板模型，以将建模工作重点放在特定于算法的细节上。为了缓解状态空间爆炸，本文提出了两种归约技术，分别是分区对称性缩减和消息顺序缩减，它们利用状态空间中的对称性来避免扩展等效状态。用于验证基于回合的算法的可重用框架和两种提出的归约技术提供了将数量级减少分析通用分布式算法所需的状态数的方法。