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

ACID Properties

Atomicity, Consistency, Isolation, Durability – fundamental properties ensuring reliable transaction processing in databases.
📜

The statement of the theorem

Let T\mathcal{T} be a transaction, Sk\mathbf{S}_{k} be the database state before T\mathcal{T}, and Sk+1\mathbf{S}_{k+1} be the state after T\mathcal{T}. The ACID properties require the following conditions:\n\n1. **Atomicity:** Commit(T)  ⟹  Sk+1=Sk after T executes fully\text{Commit}(\mathcal{T}) \implies \mathbf{S}_{k+1} = \mathbf{S}_{k} \text{ after } \mathcal{T} \text{ executes fully}. Abort(T)  ⟹  Sk+1=Sk\text{Abort}(\mathcal{T}) \implies \mathbf{S}_{k+1} = \mathbf{S}_{k}.\n2. **Consistency:** Sk+1⊨I\mathbf{S}_{k+1} \models I, where II is the set of all database invariants (constraints) that must hold true for any valid state.\n3. **Isolation:** For any set of concurrent transactions T={T1,…,Tn}\mathcal{T} = \{\mathcal{T}_1, \dots, \mathcal{T}_n\}, the resulting state Sk+1\mathbf{S}_{k+1} must be indistinguishable from the state resulting from some serial execution Sk+1=Sk after Ser(T)\mathbf{S}_{k+1} = \mathbf{S}_{k} \text{ after } \text{Ser}(\mathcal{T}).\n4. **Durability:** If Commit(T)\text{Commit}(\mathcal{T}) occurs, the changes ΔS\Delta \mathbf{S} are permanently recorded in stable storage, such that subsequent system failures do not revert Sk+1\mathbf{S}_{k+1} to Sk\mathbf{S}_{k}.