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We explore the property of equivocation tolerance for Conflict-Free Replicated Data Types (CRDTs). We show that a subclass of CRDTs is equivocation-tolerant and can thereby cope with any number of Byzantine faults: Without equivocation…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-10-11 Florian Jacob , Saskia Bayreuther , Hannes Hartenstein

Conflict-Free Replicated Data Types (CRDTs) are used in a range of fields for their coordination-free replication with strong eventual consistency. By prioritising availability over consistency under partition, peers accumulate events in…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-04-09 Kegan Dougal

Conflict-free Replicated Data Types (CRDTs) are designed for replica convergence without global coordination or consensus. Recent work has achieved the same in a Byzantine environment, through DAG-like structures based on cryptographic…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-01-23 Paulo Sérgio Almeida , Ehud Shapiro

Matrix is a new kind of decentralized, topic-based publish-subscribe middleware for communication and data storage that is getting popular particularly as a basis for secure instant messaging. In comparison to traditional decentralized…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-02-23 Florian Jacob , Carolin Beer , Norbert Henze , Hannes Hartenstein

Data replication is used in distributed systems to maintain up-to-date copies of shared data across multiple computers in a network. However, despite decades of research, algorithms for achieving consistency in replicated systems are still…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-08-30 Victor B. F. Gomes , Martin Kleppmann , Dominic P. Mulligan , Alastair R. Beresford

***** This design is a duplicate of a Causal Length Set (see notes in the comments). We leave nonetheless the original paper here because the proofs are referred to in another submission.***** The 2P-Set Conflict-Free Replicated Data Type…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-05-29 Erick Lavoie

Distributed systems designed to serve clients across the world often make use of geo-replication to attain low latency and high availability. Conflict-free Replicated Data Types (CRDTs) allow the design of predictable multi-master…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-10-13 Carlos Baquero , Paulo Sergio Almeida , Ali Shoker

Conflict-free Replicated Data Types (CRDTs) allow optimistic replication in a principled way. Different replicas can proceed independently, being available even under network partitions, and always converging deterministically: replicas…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-09-10 Paulo Sérgio Almeida

Internet-scale distributed systems often replicate data at multiple geographic locations to provide low latency and high availability, despite node and network failures. Geo-replicated systems that adopt a weak consistency model allow…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-06-28 Nuno Preguiça

Byzantine-Fault-Tolerant (BFT) systems are rapidly emerging as a viable technology for production-grade systems, notably in closed consortia deployments for nancial and supply-chain applications. Unfortunately, most algorithms proposed so…

Databases · Computer Science 2019-11-11 Loïck Bonniot , Christoph Neumann , François Taïani

Conflict-free replicated data types (CRDTs) and the local-first concept are increasingly employed not only in small-scale collaboration systems among few users who trust each other, but also in large-scale systems, like Matrix for instant…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-04-28 Florian Jacob , Johanna Stuber , Hannes Hartenstein

We study distributed optimization over networks with Byzantine agents that may send arbitrary adversarial messages. We propose \emph{Gradient Tracking with Probabilistic Edge Dropout} (GT-PD), a stochastic gradient tracking method that…

Machine Learning · Computer Science 2026-04-07 Amirhossein Dezhboro , Fateme Maleki , Arman Adibi , Erfan Amini , Jose E. Ramirez-Marquez

Trees are fundamental data structure for many areas of computer science and system engineering. In this report, we show how to ensure eventual consistency of optimistically replicated trees. In optimistic replication, the different replicas…

Data Structures and Algorithms · Computer Science 2012-01-10 Stéphane Martin , Mehdi Ahmed-Nacer , Pascal Urso

In Opportunistic Networks (OppNets), the dissemination of information can only rely on transient pairwise radio contacts between mobile devices (peers). Designing distributed applications that can run in such conditions is a challenge, but…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-05-22 Frédéric Guidec , Yves Mahéo

CRDTs are distributed data types that make eventual consistency of a distributed object possible and non ad-hoc. Specifically, state-based CRDTs ensure convergence through disseminating the entire state, that may be large, and merging it to…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-10-17 Paulo Sérgio Almeida , Ali Shoker , Carlos Baquero

This paper explores the territory that lies between best-effort Byzantine-Fault-Tolerant Conflict-free Replicated Data Types (BFT CRDTs) and totally ordered distributed ledgers, such as those implemented by Blockchains. It formally…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-03-11 Davide Frey , Lucie Guillou , Michel Raynal , François Taïani

In this paper, we study the problem of distributed training (DT) under Byzantine attacks with communication constraints. While prior work has developed various robust aggregation rules at the server to enhance robustness to Byzantine…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-04-01 Chengxi Li , Youssef Allouah , Rachid Guerraoui , Mikael Skoglund , Ming Xiao

A conflict-free replicated data type (CRDT) is an abstract data type, with a well defined interface, designed to be replicated at multiple processes and exhibiting the following properties: (1) any replica can be modified without…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-06-22 Nuno Preguiça , Carlos Baquero , Marc Shapiro

Consensus protocols are fundamental in distributed systems as they enable software with strong consistency properties. However, designing optimized protocols for specific use-cases under certain system assumptions is typically a laborious…

Programming Languages · Computer Science 2025-04-09 Julian Haas , Ragnar Mogk , Annette Bieniusa , Mira Mezini

Conflict-free replicated data types (CRDTs) are distributed data structures designed for fault tolerance and high availability. CRDTs have historically been taxonomized into state-based CRDTs, in which replicas apply updates locally and…

Programming Languages · Computer Science 2025-08-14 Nathan Liittschwager , Jonathan Castello , Stelios Tsampas , Lindsey Kuper
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