论因果一致性的验证

A. Bouajjani, C. Enea, R. Guerraoui, Jad Hamza
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引用次数: 44

摘要

因果一致性是分布式数据结构实现中最常用的一致性标准之一。它确保在所有地点按照其因果优先级执行操作。我们解决了自动验证数据结构实现的执行是否因果一致的问题。我们考虑两个问题:(1)检查单个执行是否因果一致,这与开发测试和bug查找算法有关;(2)验证一个实现的所有执行是否因果一致。我们证明了第一个问题是np完全的。这甚至适用于读写内存抽象,而读写内存抽象是许多现代分布式系统的构建块。实际上,这样的系统通常将数据存储在键值存储中,这是读写内存抽象的实例。此外,令人惊讶的是,我们证明了第二个问题是不可确定的,这一点甚至适用于读写内存抽象。然而,我们表明,对于读写内存抽象,如果实现是数据独立的,则可以避免这些负面结果,即它们的行为不依赖于每个时刻写入或读取的数据值,这是一个现实的假设。我们证明了对于数据独立的实现,在读写内存抽象的情况下检查单个执行正确性的问题是多项式时间。此外,我们证明了对于这样的实现,非因果一致执行的集合可以用有限数量的寄存器自动机来表示。使用这些机器作为观察者(与实现并行)可以将检查因果一致性的问题多项式地减少为状态可达性问题。无论用于实现的程序的类别、读写变量的数量以及使用的数据域如何,这种减少都是有效的。它允许利用现有的断言/可达性检查技术进行因果一致性验证。此外,对于一类重要的实现,我们从这种约简中得出验证因果一致性的可判定性,而不是读写内存抽象。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On verifying causal consistency
Causal consistency is one of the most adopted consistency criteria for distributed implementations of data structures. It ensures that operations are executed at all sites according to their causal precedence. We address the issue of verifying automatically whether the executions of an implementation of a data structure are causally consistent. We consider two problems: (1) checking whether one single execution is causally consistent, which is relevant for developing testing and bug finding algorithms, and (2) verifying whether all the executions of an implementation are causally consistent. We show that the first problem is NP-complete. This holds even for the read-write memory abstraction, which is a building block of many modern distributed systems. Indeed, such systems often store data in key-value stores, which are instances of the read-write memory abstraction. Moreover, we prove that, surprisingly, the second problem is undecidable, and again this holds even for the read-write memory abstraction. However, we show that for the read-write memory abstraction, these negative results can be circumvented if the implementations are data independent, i.e., their behaviors do not depend on the data values that are written or read at each moment, which is a realistic assumption. We prove that for data independent implementations, the problem of checking the correctness of a single execution w.r.t. the read-write memory abstraction is polynomial time. Furthermore, we show that for such implementations the set of non-causally consistent executions can be represented by means of a finite number of register automata. Using these machines as observers (in parallel with the implementation) allows to reduce polynomially the problem of checking causal consistency to a state reachability problem. This reduction holds regardless of the class of programs used for the implementation, of the number of read-write variables, and of the used data domain. It allows leveraging existing techniques for assertion/reachability checking to causal consistency verification. Moreover, for a significant class of implementations, we derive from this reduction the decidability of verifying causal consistency w.r.t. the read-write memory abstraction.
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