Abstract
Any computing system can be described as executing sequences of actions, with an action being any relevant change in the state of the system. For example, reading a file to memory, modifying the contents of the file in memory, or writing the new contents to the file are relevant actions for a text editor. In a distributed system, actions execute in multiple locations; in this context, actions are often called events. Examples of events in distributed systems include sending or receiving messages, or changing some state in a node. Not all events are related, but some events can cause and influence how other, later events occur. For example, a reply to a received mail message is influenced by that message, and maybe by prior messages received.

Abstract
Conflict-free Replicated Data Types (CRDTs) are data abstractions (registers, counters, sets, maps, among others) that provide a relaxed consistency model called Eventual Consistency. Current designs for CRDT counters do not scale, having a size linear with the number of both active and retired nodes (i.e., nodes that leave the system permanently after previously manipulating the value of the counter). In this paper we present a new counter design called Borrow-Counter, that provides a mechanism for the retirement of transient nodes, keeping the size of the counter linear with the number of active nodes.

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.