Relaxing real-time order in opacity and linearizability

In this paper we introduce two families of safety properties: ♦-opacity and ♦linearizability. The new properties relax to various degree the real-time order requirement on transaction execution in opacity and, analogically, the real-time order requirement on operation execution in linearizability. This way we can formalize the guarantees provided by a wide class of strongly consistent replicated systems for which opacity and linearizability are too strong. As an example, we analyze Deferred Update Replication, a well known optimistic concurrency control scheme, and prove it satisfies update-real-time opacity, which allows readonly and aborted transactions to operate on stale (but still consistent) data. We also show the relationship between ♦-opacity and ♦-linearizability.