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In the read phase, write operations write to local memory, in the validation phase it is investigated if the transaction conflicts with other transactions and if it can continue to its write phase where writes are made global. One of the following three conditions must hold (τi is the validating transaction and τj is any other active transaction, and rs(τ ) and ws(τ ) are the read set and write set of τ respectively) [38]: (i) the write phase of τi completes before the read phase of τj starts, (ii) ws(τi ) ∩ rs(τj ) = ∅ and the write phase of τi completes before the write phase of τj , and (iii) ws(τi ) ∩ ws(τj ) = ∅ ∧ ws(τi ) ∩ rs(τj ) = ∅ and the read phase of τi completes before the read phase of τj .
The validity of data items using the time domain has been studied in the real-time community [5, 7, 15, 23, 24, 35, 36, 44, 50, 55, 66, 67]. A continuous data item is said to be absolutely consistent with the entity it represents as long as the age of the data item is below a predefined limit [55]. 1 (Absolute Consistency). Let x be a data item. Let timestamp(x) be the time when x was created and avi(x), the absolute validity interval, be the allowed age of x. Data item x is absolutely consistent when: current_time − timestamp(x) ≤ avi(x).
If value 50 is similar to value 55, it would be strange if value 55 is not similar to value 50. Thus, relation f is symmetric. 3 is reflexive, symmetric and transitive, but a similarity relation does not need to be transitive. , |5 − 7| ≤ 3, |7 − 9| ≤ 3, but |5 − 9| ≤ 3. The intervals where two temperatures are considered to be similar might be entries in a lookup table, thus, all temperatures within the same interval result in the same value to be fetched from the table, motivating why similarity works in real-life applications.