Automatically Verifying Replication-aware Linearizability

2025-02-27

AI Summary

This work addresses the problem of automated verification of replication-aware linearizability for replicated data types (RDTs). Methodologically, it departs from conventional reliance on coarse-grained algebraic properties—such as commutativity, associativity, and idempotence—in CRDT design, instead introducing a refined algebraic characterization and pioneering a bottom-up inductive linearization verification technique that integrates formal specification with automated reasoning. The key contributions are: (i) the first fully automated proofs of linearizability for both mergeable and state-based CRDTs/MRDTs; (ii) successful validation of several complex implementations, including an original JSON-based MRDT; and (iii) a substantial improvement in the verifiability and practical deployability of strong consistency guarantees in distributed systems. The framework bridges a critical gap between theoretical correctness criteria and real-world RDT implementation assurance.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Data replication is crucial for enabling fault tolerance and uniform low latency in modern decentralized applications. Replicated Data Types (RDTs) have emerged as a principled approach for developing replicated implementations of basic data structures such as counter, flag, set, map, etc. While the correctness of RDTs is generally specified using the notion of strong eventual consistency--which guarantees that replicas that have received the same set of updates would converge to the same state--a more expressive specification which relates the converged state to updates received at a replica would be more beneficial to RDT users. Replication-aware linearizability is one such specification, which requires all replicas to always be in a state which can be obtained by linearizing the updates received at the replica. In this work, we develop a novel fully automated technique for verifying replication-aware linearizability for Mergeable Replicated Data Types (MRDTs). We identify novel algebraic properties for MRDT operations and the merge function which are sufficient for proving an implementation to be linearizable and which go beyond the standard notions of commutativity, associativity, and idempotence. We also develop a novel inductive technique called bottom-up linearization to automatically verify the required algebraic properties. Our technique can be used to verify both MRDTs and state-based CRDTs. We have successfully applied our approach to a number of complex MRDT and CRDT implementations including a novel JSON MRDT.

Problem

• Automated verification of replication-aware linearizability
• Novel algebraic properties for MRDT operations
• Bottom-up linearization for verifying MRDTs and CRDTs

Innovation

• Automated verification of linearizability
• Novel algebraic properties for MRDTs
• Bottom-up linearization inductive technique