Snapshot Equivalence

Synonyms

Temporally weak; Weak equivalence

Definition

Informally, two tuples are snapshot equivalent or weakly equivalent if all pairs of timeslices with the same time instant parameter of the tuples are identical.

Let temporal relation schema R have n time dimensions, $Di,i=1,\dots, n$, and let $\tau i,i=1,\dots, n$ be corresponding timeslice operators, e.g., the valid timeslice and transaction timeslice operators. Then, formally, tuples x and y are snapshot equivalent if

$$ \begin{array}{l} \forall {t}_1\in {D}_1\dots \forall {t}_n\in {D}_n\left({\tau}_{t_n}^n\left(\dots \left({\tau}_{t_1}^1(x)\right)\right)\dots \right)\\ ={\tau}_{t_n}^n\left(\dots \left({\tau}_{t_1}^1(y)\right)\dots \Big)\right)\end{array} $$

Similarly, two relations are snapshot equivalent or weakly equivalent if at every instant their snapshots are equal. Snapshot equivalence, or weak equivalence, is a binary relation that can be applied to tuples and to relations.

Key Points

The notion of weak...