On Verifying Causal Consistency

TL;DR

This paper investigates the complexity of verifying causal consistency in distributed data structures, proving NP-completeness for single execution checks and undecidability for universal verification, with practical solutions for data-independent systems.

Contribution

It establishes the computational hardness of verifying causal consistency and introduces conditions under which these problems become tractable.

Findings

Checking a single execution's causal consistency is NP-complete.

Verifying all executions' causal consistency is undecidable.

Data independence allows circumventing negative results in verification.

Abstract

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.