Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Concurrency Control

Mechanisms (e.g., locking) to manage simultaneous access and modification of data by multiple transactions.
📜

The statement of the theorem

Let T1,T2\mathcal{T}_1, \mathcal{T}_2 be two concurrent transactions operating on a data item XX. Define the conflict set C(X)={(Read(X),Write(X)),(Write(X),Read(X)),(Write(X),Write(X))}C(X) = \{(\text{Read}(X), \text{Write}(X)), (\text{Write}(X), \text{Read}(X)), (\text{Write}(X), \text{Write}(X))\}. A concurrency control mechanism M\mathcal{M} must ensure that for every pair of conflicting operations o1∈Op(T1)o_1 \in \text{Op}(\mathcal{T}_1) and o2∈Op(T2)o_2 \in \text{Op}(\mathcal{T}_2), the mechanism enforces a total ordering ≺\prec such that the execution sequence respects the defined conflict resolution rules (e.g., two-phase locking: Lock(X)\text{Lock}(X) must be acquired before Read(X)\text{Read}(X) or Write(X)\text{Write}(X)).