Serializability is a concept of database theory for handling concurrent transactions. You don't have to understand it to use locks well, but in case you want to know a little more background: A schedule of concurrent transactions is called serializeable if there exists an equivalent, serial schedule of the same transactions. In other words: the schedules are serializable if the operations of all transactions can be reordered in such a way that afterwards the transactions can be executed completely one after another. If a schedule is serializable, it is correct (i.e. maintains the ACID principles) and all transactions of the schedule can commit. If a schedule is not serializable, the schedule might be incorrect and at least one transaction has to be aborted.

There exist various definitions for the above mentioned equivalence of two schedules. Depending on which definition is chosen, different kinds of serializability arise:

State serializability
Based on state equivalence; Two schedules are state-equivalent if for all possible start states both schedules reach a common end state.
View serializability
Based on view equivalence; Two schedules are view-equivalent if they are state-equivalent and all read operations in both schedules read the value written by the same write operation (i.e. they see the same view of the data). Please note that if both schedules write all used data at their beginning and read all changed data at the end, state equivalence is enforced implicitly and then doesn't have to be demanded in the view equivalence definition.
Conflict serializability
Based on conflict equivalence; Two schedules are conflict-equivalent if the order of all conflicting operations of concurrent transactions is the same in both. Normally a read and a write operations on the same data conflict with each other as well as two write operations.

It can be shown that a subset relationship exists between the sets of schedules which fulfill these three serializability criteria: The conflict-serializable schedules are a subset of the view-serializable schedules, which are a subset of the state-serializable schedules, which in turn are a subset of all correct schedules. So it would be best to test for state serializability since that would allow the most concurrency. Alas it can also be shown that checking for state serializability and view serializability is NP-complete. For this reason all commercial RDBMSs use AFAIK conflict serializability which can be enforced by two-phase locking with read and write locks.

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