A transaction is a unit of program execution that reads and possibly updates database items and must behave as one indivisible step: either all of its effects persist or none do, and other transactions see it as if it ran alone.
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Isolation says that concurrent transactions must behave as if they ran one at a time. Serializability makes this precise: a schedule is acceptable if it is equivalent to some serial schedule. Two notions of equivalence are used.
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Serializability ignores failures: it assumes every transaction commits. A real system must also handle a transaction that aborts after other transactions have read what it wrote. Recoverability classifies schedules by how safely they survive such aborts, using the positions of commits and aborts.
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