Let T be a transaction composed of subtransactions S0, S1, …Sn−1. Let C0, C1, …Cn−1 be a set of compensating transactions, such that Ci compensates for the corresponding Si. T is semantically atomic iff all Si have committed, or for all Si that have committed, Ci has also committed. A schedule (or history) ensures semantic atomicity if all transactions are semantically atomic. If T requires compensating transactions, then the resulting database is semantically equivalent to one in which T did not execute at all, but it is not guaranteed to be identical. Typically, two database states are equivalent if they both satisfy all of the database constraints.
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