Conflict-Free Replicated Information Types

Below are my notes summarizing the newspaper "Conflict-free Replicated Data Types" past times Marc Shapiro, Nuno Preguica, Carlos Baquero, too Marek Zawirski. The newspaper is available here.

Replicated soil machines (RSMs) are a basic too of import tool for distributed systems. The persuasion inwards RSMs is if the replicas start from the same initial soil too perform the same updates amongst the same order, thence their terminate states are the same. The "strong consistency" approach provides this guarantee past times serializing updates to the replicas inwards a global full order. However, the downwards side to strong consistency approach is that it is a performance & scalability bottleneck, too it also conflicts amongst availability too partition-tolerance (due to the CAP theorem).

Replicating information nether Eventual Consistency (EC) allows whatever replica to bring updates without remote synchronization. However, published EC approaches are ad-hoc too error-prone (they come upward without a formal proof of corrrectness). CRDT operate tries to address this work past times proposing a uncomplicated formally-proven approach to EC, called Strong Eventual Consistency (SEC), which avoids the complexity of conflict-resolution too roll-back.

SEC defines a stronger convergence holding than EC. SEC states that right replicas that conduct hold delivered the same updates conduct hold equivalent soil "immediately", whereas EC states this "eventually" ---since conflict recovery needs to live performed across replicas. (Actually Strong Eventual "Convergence" is a to a greater extent than appropriate too accurate term to pull SEC than Strong Eventual Consistency, because SEC does non genuinely ameliorate the consistency over EC.)

SEC obviates the postulate for the replicas to coordinate for conflict recovery because it provides conflict-freedom past times leveraging on monotonicity inwards a semi-lattice or commutativity (a piddling illustration to this is a "set" information type). On the other hand, the downside to SEC too the CRDT approach is that the applicability is express to uncomplicated locally verifiable invariants. In other words, conflict-freedom is traded off amongst meaningful & useful invariants that bridge across replicas: When a replica is at a item state, it is difficult to soil whatever predicate virtually the soil of the other replicas. (Note that, inwards strong consistency---achieved using Paxos for example--- you lot could soil that the soil of all replicas are equal. CRDT is PAEL too Paxos is PCEC.)

In the residuum of the paper, 2 sufficient weather condition are presented for SEC ---a state-based implementation of CRDT too an operation-based implementation of CRDT--- too a strong equivalence betwixt the 2 weather condition is proven.

State-based replication

Executing an update modifies the soil of a unmarried replica. Using gossip protocols, every replica occasionally sends its local soil to another replica, which merges this soil into its ain state. Every update eventually reaches every replica, either straight or indirectly. (For efficiency, the metadata of the object to live replicated may live gossiped first.)

A semilattice is a partial gild ≤ equipped amongst a to the lowest degree upper saltation (LUB) for all pairs. LUB is commutative, idempotent, too associative. Monotonic semi-lattice is where (i) The soil laid south forms a semilattice ordered past times ≤. (ii) Merging soil sec amongst remote soil s' computes the LUB of the 2 states. (iii) State is monotonically non-decreasing across updates, i.e., sec ≤ sec + u.

Theorem 1 (Convergent Replicated Data Type (CvRDT)). Assuming eventual delivery too termination, whatever state-based object that satisfies the monotonic semilattice holding is SEC.

At this betoken it is of import to Federal Reserve annotation that monotonic semilattice holding is non a uncomplicated property, because providing a LUB for all soil pairs bring around pains. For instance, a uncomplicated diamond tiling lattice does non satisfy this property.

Operation-based replication

Alternative to the state-based style, a replicated object may live specified inwards the operation-based style. An op-based object has no merge method; instead an update is dissever into a distich (t, u), where t is a side-effect-free prepare-update method too u is an effect-update method. The effect-update method executes at all downstream replicas. A sufficient status for convergence of an op-based object is that "all" its concurrent operations commute. An object satisfying this status is called a Commutative Replicated Data Type (CmRDT).

Theorem 2 (Commutative Replicated Data Type (CmRDT)). Assuming causal too exactly-once delivery of updates too method termination, whatever op-based object that satisfies the commutativity holding for all concurrent updates, too whose delivery precondition is satisfied past times causal delivery, is SEC.

CvRDTs too CmRDTs are equivalent

The equivalence means, nosotros tin rewrite a CvRDT every bit a CmRDT, too vice a versa, amongst around effort. The proofs inwards the newspaper essentially exhibit that this tin live done, albeit inwards an inefficient manner. To give around intuition virtually this equivalence, let's compare a CmRDT counter implementation versus a CvRDT counter implementation below.

A CmRDT counter is real uncomplicated to implement, when you lot larn a novel increment functioning delivered only increment your counter past times 1. If nosotros unequivocally seat every functioning too the delivery pre-condition guarantees that all operations are delivered too executed precisely in i trial through the causally-ordered broadcast middleware, replicas volition converge regardless of whatever gild operations are applied. We conduct hold SC.

A CvRDT monotonic counter is non that piddling to implement: Consider a counter that maintains the issue of increments. To merge the value (i.e., state) of 2 replicas amongst value 1, nosotros could heart the values, or select the maximum value of the merging replicas, but neither would render the right value inwards every case: If the replicas had concurrent updates, thence the value should live 2. However, if the 2 replicas are readily synchronized (through gossip), the lastly value should live 1. This arrive impossible to purpose either max or heart every bit the merge procedure. Instead, the right solution is inspired past times vector clocks: Store the issue of increments for each replica indexed past times seat inwards a vector. The inquiry functioning retrieves the heart of every vector seat too the merge physical care for selects the maximum value for each index inwards the vector.

So what happens is this. In gild to avoid soil replication, CmRDT assumes an underlying reliable causally-ordered broadcast communication middleware; i that delivers every message to every recipient precisely in i trial too inwards an gild consistent amongst happened-before. This is genuinely hiding soil nether the rug, because frequently (for most examples) the causally-ordered broadcast communication middleware requires the replicas to proceed version vectors, too to buffer/wait operations earlier delivering (as long every bit it takes) to ensure that all the operations that causally-precede these operations are delivered first.

Concluding remarks

CRDT provides a express remedy to CAP theorem. A CRDT replica is ever available for both reads too writes, independently of network conditions. Any communicating subset of replicas of a SEC object eventually converges, fifty-fifty if partitioned from the residuum of the network. This is non inwards whatever way at odds amongst the CAP theorem, because CRDT weakens consistency to render to a greater extent than availability. The consistency is weakened thence much that it is non possible to render an invariant that spans acrosss replicas. To address the useful invariants problem, futurity operate prescribes investigating stronger global invariants (using probabilistic or heuristic techniques), too supporting infrequent, non-critical synchronous operations (such every bit committing a soil or performing a global reset).

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