Relaxed Memory Model Zoo

Causal+ (Convergent Causal) Consistency
← Back to the map

Causal+ (Convergent Causal) Consistency

2011 · Lloyd, Freedman, Kaminsky, Andersen · theoretical, formal · axiomatic formalism

Convergent causal consistency, introduced with the COPS wide-area store. It augments causal consistency with strong convergence: replicas that have applied the same set of writes have equivalent state, so concurrent (causally unrelated) conflicting writes are resolved identically at every replica via commutative/associative handler functions. Viotti & Vukolić (ACM Computing Surveys 2016, Eq. 27) express it as Causal+ = Causality ∧ StrongConvergence, i.e. causal+ strengthens causal consistency exactly as strong eventual consistency strengthens eventual consistency, so it is strictly stronger than causal consistency. Incomparable to real-time causal consistency.

Properties

Property vector author-extrapolated — set only where the model’s definition pins the cell down (unknown cells are omitted); cells citing a specific source are marked.

Reasoning guarantees
  • no Coherence
Atomicity guarantees
  • no Multicopy atomic

Ordering relationships

Strictly stronger than
  • Causal Consistency — Causal+ = Causality ∧ StrongConvergence (Viotti & Vukolić 2016, Eq. 27; Lloyd et al., COPS, SOSP 2011). It adds strong convergence (all replicas that applied the same writes have equivalent state) on top of causal consistency, disallowing strictly more behaviours, so causal consistency is strictly weaker than causal+.
Incomparable with
  • Real-Time Causal Consistency (RTCausal) — Causal+ and real-time causal consistency are incomparable (Viotti & Vukolić 2016, §3.5): real-time causality does not imply strong convergence, and causal+ does not impose real-time ordering — each forbids a behaviour the other allows. (V-V correct Lloyd et al.'s original claim that real-time causal is stronger than causal+.)

References

  • Wyatt Lloyd, Michael J. Freedman, Michael Kaminsky, David G. Andersen. Don't Settle for Eventual: Scalable Causal Consistency for Wide-Area Storage with COPS. SOSP 2011, 2011. doi:10.1145/2043556.2043593
  • Paolo Viotti, Marko Vukolić. Consistency in Non-Transactional Distributed Storage Systems. ACM Computing Surveys 49(1), 2016. doi:10.1145/2926965