[论文解读] On distributed monitoring of asynchronous systems

Volker Diekert, Anca Muscholl|arXiv (Cornell University)|Aug 10, 2012

Advanced Data Processing Techniques参考文献 21被引用 8

一句话总结

本文提出了一种基于异步自动机的异步系统分布式运行时监控框架，引入了局部可监控迹语言的概念。证明了可表达为可数个局部安全语言并集的性质——特别是那些在Γ-无限迹上既确定又共确定的性质——是局部可监控的，为在无全局观测条件下验证分布式系统奠定了基础性结果。

ABSTRACT

Distributed systems are notoriously difficult to understand and analyze in order to assert their correction w.r.t. given properties. They often exhibit a huge number of different behaviors, as soon as the active entities (peers, agents, processes, etc) behave in an asynchronous manner. Already the modelization of such systems is a non-trivial task, let alone their formal verification. The purpose of this paper is to discuss the problem of distributed monitoring on a simple model of finite-state distributed automata based on shared actions, called asynchronous automata. Monitoring is a question related to runtime verification: assume that we have to check a property $L$ against an unknown or very complex system $A$, so that classical static analysis is not possible. Therefore instead of model-checking a monitor is used, that checks the property on the underlying system at runtime. We are interested here in monitoring distributed systems modeled as asynchronous automata. It is natural to require that monitors should be of the same kind as the underlying system, so we consider here distributed monitoring. A distributed monitor does not have a global view of the system, therefore we propose the notion of locally monitorable trace language. Our main result shows that if the distributed alphabet of actions is connected and if $L$ is a set of infinite traces such that both $L$ and its complement $L^c$ are countable unions of locally safety languages, then $L$ is locally monitorable. We also show that over infinite traces, recognizable countable unions of locally safety languages are precisely the complements of deterministic languages.

研究动机与目标

• 定义一种适用于无全局可见性监控器的异步系统分布式监控概念。
• 形式化局部可监控迹语言的概念，作为全局可监控性的对应概念。
• 识别在分布式、去中心化方式下可监控性质的充分条件。
• 通过PGδ ∩ PFσ集合建立可识别语言与局部可监控性质类之间的联系。

提出的方法

• 基于共享动作和带位置函数的分布式字母表，引入异步自动机以定义过程依赖关系。
• 定义Mazurkiewicz迹及其前缀，以建模具有独立关系的并发行为。
• 引入素迹（prime traces）及素开/闭集，以在Scott拓扑中形式化局部安全性质。
• 使用PGδ ∩ PFσ类（Gδ集的可数交集与Fσ集的可数并集）来刻画局部可监控语言。
• 证明：若语言L及其补集均为Γ-无限迹上局部安全语言的可数并集，则L是局部可监控的。
• 建立：在Γ-无限迹背景下，可识别的局部安全语言的可数并集恰好等于确定性语言的补集。

实验结果

研究问题

• RQ1 在无全局视图的分布式环境中，哪些性质可被监控？
• RQ2 在异步、基于迹的系统中，如何形式化局部安全性？
• RQ3 在缺乏全局系统观测的情况下，迹语言在何种条件下是局部可监控的？
• RQ4 确定性/共确定性语言与局部可监控性质类之间存在何种关系？
• RQ5 是否能通过拓扑与自动机理论构造完全刻画局部可监控语言类？

主要发现

• 若语言L及其补集均为Γ-无限迹上局部安全语言的可数并集，则L是局部可监控的。
• Γ-无限迹上的局部可监控语言类与PGδ ∩ PFσ集合完全一致。
• 在Γ-无限迹背景下，可识别的局部安全语言的可数并集恰好是确定性语言的补集。
• 若一个确定性异步Büchi自动机的语言是共确定的，则其语言是局部可监控的。
• 分布式字母表的连通性对于主要结果至关重要，但该假设在更广泛类中的必要性仍待开放。
• 该框架通过将监控简化为基于迹前缀与进程本地状态的本地、去中心化检查，支持分布式系统的自动化验证。