A Semantic Approach to Correctness of Concurrent Transaction Executions
A Semantic Approach to Correctness of Concurrent Transaction Executions
Paul G Spirakis
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Definition . A schedule S is independent iff each transaction T of S is independent in S. Let I be the class of Independent schedules. Definition . A schedule is correct iff (1) it is independent (2) it preserves ICs, and (3) it has no racing. Let C be the class of correct schedules. The following proposition is immediate. -13- Proposttlon . Independent schedules cannot produce Inconsistent outputs to the user. However, the Inverse is not true. Here Is a counterexample: 1 Tl T2 1 1 rA 1 rB rA 1... rB 1 A := A - A 1 wA ! 1 rA B := B + A 1 wB 1 1 output B T, produces a consistent output but it cannot be independent. Here, this happens because of multiple reads allowed to be in sequence in a transaction. Therefore, our class, C, of correct schedules is a subset of the class of schedules without inconsistencies. (If we were following the approach of defining independence in terms of transaction external writes, we would have captured, in the class of correct schedules, all the schedules which avoid all types of inconsistencies.
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