Abstract
Conflict-free Data Types (CRDTs) were designed to automatically resolve conflicts in eventually consistent systems. Different CRDTs were designed in both operation-based and state-based flavors such as Counters, Sets, Registers, Maps, etc. In a previous paper [2], Baquero et al. presented the problem with embedded CRDT counters and a solution, covering state-based counters that can be embedded in maps, but needing an ad-hoc extension to the standard counter API. Here, we present a resettable operation-based counter design, with the standard simple API and small state, through a causal-stability-based state compaction.

Abstract
Eventual consistency is a relaxed consistency model used in large-scale distributed systems that seek better availability when consistency can be delayed. CRDTs are distributed data types that make eventual consistency of a distributed object possible and non ad-hoc. Specifically, state-based CRDTs achieve this through shipping the entire replica state that is, eventually, merged to other replicas ensuring conver- gence. This imposes a large communication overhead when the replica size or the number of replicas gets larger. In this work, we introduce a decomposable version of state-based CRDTs, called Delta State-based CRDTs (d-CRDT). A d-CRDT is viewed as a join of multiple fine-grained CRDTs of the same type, called deltas (d). The deltas are produced by applying d-mutators, on a replica state, which are mod- ified versions of the original CRDT mutators. This makes it possible to ship small deltas (or batches) instead of ship- ping the entire state. The challenges are to make the join of deltas equivalent to the join of the entire object in clas- sical state-based CRDTs, and to find a way to derive the d-mutators. We address this challenge in this work, and we explore the minimal requirements that a communication al- gorithm must offer according to the guarantees provided by the underlying messaging middleware. Copyright © 2007 by the Association for Computing Machinery, Inc.

Abstract
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 other replicas; whereas operation-based CRDTs disseminate operations (i.e., small states) assuming an exactly-once reliable dissemination layer. We introduce Delta State Conflict-Free Replicated Datatypes (d-CRDT) that can achieve the best of both worlds: small messages with an incremental nature, disseminated over unreliable communication channels. This is achieved by defining d-mutators to return a delta-state, typically with a much smaller size than the full state, that is joined to both: local and remote states. We introduce the d-CRDT framework, and we explain it through establishing a correspondence to current state-based CRDTs. In addition, we present an anti-entropy algorithm that ensures causal consistency, and two d-CRDT specifications of well-known replicated datatypes. © Springer International Publishing Switzerland 2015.

Abstract
Conict-free Replicated Datatypes can simplify the design of predictable eventual consistency. They can be classified into state-based or operation-based. Operation-based ap- proaches have the potential for allowing compact designs in both the sent message and the object state size, but cur- rent approaches are still far from this objective. Here we explore the design space for operation-based solutions, and we leverage the interaction with the middleware by offering a technique that delivers very compact solutions, while only broadcasting operation names and arguments. Copyright © 2007 by the Association for Computing Machinery, Inc.

Abstract
Conflict-free Replicated Datatypes (CRDT) are usually classified as either state-based or operation-based. However, the standard definition of op-based CRDTs is very encompassing, allowing even sending the full-state, blurring the distinction. We introduce pure op-based CRDTs, that can only send operations to other replicas, drawing a clear distinction from state-based ones. Datatypes with commutative operations can be trivially implemented as pure op-based CRDTs using standard reliable causal delivery. We propose an extended API - tagged reliable causal broadcast - that provides causality information upon delivery, and show how it can be used to also implement other datatypes having non-commutative operations, through the use of a PO-Log - a partially ordered log of operations - inside the datatype. A semanticallybased PO-Log compaction framework, using both causality and what we denote by causal stability, allows obtaining very compact replica state for pure op-based CRDTs, while also benefiting from small message sizes.

Abstract
To achieve high availability in the face of network partitions, many distributed databases adopt eventual consistency, allow temporary conflicts due to concurrent writes, and use some form of per-key logical clock to detect and resolve such conflicts. Furthermore, nodes synchronize periodically to ensure replica convergence in a process called anti-entropy, normally using Merkle Trees. We present the design of Dotted-DB, a Dynamo-like key-value store, which uses a novel node-wide logical clock framework, overcoming three fundamental limitations of the state of the art: (1) minimize the metadata per key necessary to track causality, avoiding its growth even in the face of node churn; (2) correctly and durably delete keys, with no need for tombstones; (3) offer a lightweight antientropy mechanism to converge replicated data, avoiding the need for Merkle Trees. We evaluate DottedDB against MerkleDB, an otherwise identical database, but using per-key logical clocks and Merkle Trees for anti-entropy, to precisely measure the impact of the novel approach. Results show that: causality metadata per object always converges rapidly to only one id-counter pair; distributed deletes are correctly achieved without global coordination and with constant metadata; divergent nodes are synchronized faster, with less memory-footprint and with less communication overhead than using Merkle Trees.