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BASE Properties

A set of properties (Basically Available, Soft state, Eventually consistent) that guide the design and operation of NoSQL databases.
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The statement of the theorem

Let St\mathcal{S}_t be the system state at time tt, and St+1\mathcal{S}_{t+1} be the state after an update operation ω\omega. The system adheres to eventual consistency if, for any two updates ω1\omega_1 and ω2\omega_2 applied at times t1t_1 and t2t_2 respectively, the state St\mathcal{S}_t converges to a final state S∞\mathcal{S}_{\infty} such that: lim⁡t→∞Distance(St,S∞)=0\lim_{t \to \infty} \text{Distance}(\mathcal{S}_t, \mathcal{S}_{\infty}) = 0 where Distance(⋅,⋅)\text{Distance}(\cdot, \cdot) is a metric defined over the state space. Furthermore, the system must maintain availability AA such that for any non-failing node nin_i, the operation Read(ni)\text{Read}(n_i) or Write(ni)\text{Write}(n_i) returns a result within finite time, regardless of the consistency level achieved at time tt.