crdt design

This work addresses the challenge of modeling and verifying the semantics of concurrent updates in distributed, local-first collaborative systems. It proposes a declarative framework based on Datalog that, for the first time, systematically encodes the semantics of Conflict-Free Replicated Data Types (CRDTs) and their compositions into executable logic programs. By explicitly representing operational contexts, the framework captures concurrent behaviors and enables compositional analysis. Integrated with property-driven testing, the approach is validated in a collaborative graph editing scenario, demonstrating correctness and exhibiting strong scalability with respect to both the number of operations and replicas.

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.

This work addresses the scalability limitations of existing sequence CRDTs, which suffer from identifier bloat and excessive memory consumption under high concurrency and prolonged collaborative editing. To overcome these challenges, we introduce the Extended Stern-Brocot Tree (ESBT) into sequence CRDT design, proposing a mathematically grounded mechanism for dense, deterministic, and compact identifier allocation. Our approach ensures strong eventual consistency and convergence independent of operation order while effectively curbing identifier growth. Experimental results demonstrate that, under 100,000 concurrent operations, our method achieves 28%–88% faster response times and reduces identifier memory usage by 50%–92.81% compared to state-of-the-art alternatives such as Logoot and LSEQ, with particularly pronounced advantages in adversarial scenarios involving frequent mid-sequence insertions.

This work addresses the fundamental limitations of existing neural network model merging strategies—none of the 26 current approaches satisfy commutativity, associativity, and idempotence, thereby failing to prevent conflicts in distributed settings. To resolve this, the paper introduces CRDTMergeState, the first framework to apply Conflict-Free Replicated Data Type (CRDT) theory to model merging. It features a two-layer architecture: the first layer employs an OR-Set to enable conflict-free merging of contribution sets, while the second layer leverages Merkle-root-seeded randomness and canonical ordering to deterministically encapsulate any existing merge strategy. The approach is fully compatible with all prior methods without degrading downstream performance and guarantees strong eventual consistency. Extensive evaluation across tensors, a 7.24B-parameter model, and a 100-node network—including 104 tests and 43,368 property verifications—confirms correctness; CRDT overhead remains below 0.5 ms, achieving byte-level output consistency.

In collaborative text editing, concurrent insertions at identical positions by multiple users frequently cause interleaved text segments, degrading readability—a longstanding challenge for both CRDT and operational transformation (OT) approaches. This paper introduces “Max-Non-Interleaving,” the first formal correctness criterion capturing the essential requirement to prevent semantic corruption due to insertion interleaving. Building upon this principle, we design two CRDT algorithms: Fugue, optimized for efficiency and practical deployment, and FugueMax, which strictly satisfies Max-Non-Interleaving. Both employ position-aware sequence representations and partial-order-based merging, enabling decentralized operation and strong eventual consistency. Experimental evaluation shows that Fugue matches the performance of state-of-the-art CRDT text libraries, while FugueMax consistently produces semantically intact and human-readable merged texts under high concurrency—resolving the interleaving problem rigorously, both theoretically and empirically, for the first time.

This work addresses the limitations of existing decentralized identifiers (DIDs), which rely on blockchain or other coordination mechanisms for document updates, often incurring high costs, latency, or immutability. The paper introduces did:crdt, the first DID method leveraging signed Conflict-Free Replicated Data Types (CRDTs) to enable concurrent, coordinator-free updates without requiring global ordering, ledgers, or external consensus. By employing deterministic merging, the approach ensures Byzantine fault tolerance while supporting limited recovery after key compromise and entirely eliminating dependence on coordination infrastructure. A Rust-based implementation integrates causally ordered incremental signatures and property-based testing, achieving microsecond-scale merge operations. The system’s convergence and security properties are formally verified, and it fully complies with the W3C DID Core specification.

Traditional CRDTs struggle to ensure state consistency in Byzantine environments due to their reliance on update filtering mechanisms. This work proposes a deterministic state reconstruction approach that decouples update propagation from state derivation: all updates are accepted, but only valid ones contribute to the final state. By structurally rejecting or transforming malicious updates, the system guarantees convergence of replicas under arbitrary update injection and supports a layered security model encompassing authentication, authorization, and confidentiality. Built upon delta-state CRDTs, the resulting Melda system is tailored for JSON documents and formally verified to preserve state consistency despite message reordering, loss, or forgery. Theoretical analysis confirms that identical update sets yield indistinguishable states, achieving coordination-free strong eventual consistency with Byzantine fault tolerance.

This work addresses the challenge of seamless evolution in distributed systems undergoing backward-incompatible software updates by proposing a novel approach that models application code and its semantic versioning as an App CRDT (Conflict-Free Replicated Data Type). Coupled with an API-compatible message middleware, this mechanism enables the system to remain operational even when only a subset of its components has been updated. The study pioneers the application of CRDT principles to the dynamic replication and management of executable code, effectively tolerating backward-incompatible changes while preserving system availability. The method is implemented in the AmbientTalk language with minimal modifications to existing applications and further validated for cross-language applicability through integration with the LuAT framework.

This work addresses the challenge of securely excluding historical updates from compromised nodes in traditional Byzantine fault-tolerant CRDTs without violating causal consistency. The authors propose a fine-grained trust model that, for the first time in Byzantine CRDTs, decouples identity trust from content trust. By integrating deterministic reconstruction, public-key-based identity verification, and a semantics-aware update filtering mechanism, the approach enables selective inclusion or exclusion of updates. This design supports application-level policies and effectively mitigates Byzantine behavior and faulty nodes while strictly preserving causal consistency, thereby significantly enhancing the robustness and flexibility of decentralized systems in post-compromise scenarios.

Existing Byzantine fault-tolerant CRDT systems lack evolvable and replicable state management for trust relationships and governance rules. This work proposes a dual-CRDT architecture: a Trust CRDT models governance policies and trust relations as dynamically evolvable CRDT states, while a Data CRDT deterministically reconstructs its state based on this trust configuration, enabling co-evolution of governance and data. By incorporating governance itself into the CRDT state, the design introduces a recursive trust governance model augmented with a Byzantine trust filtering mechanism. A prototype implementation on the Melda/melda-sec platform demonstrates the feasibility of self-consistent, evolvable trust governance in decentralized environments.