Conflict Equivalent
Two schedules are said to be conflict equivalent when one can be transformed to another by swapping non-conflicting operations. In the example discussed above, S11 is conflict equivalent to S1 (S1 can be converted to S11 by swapping non-conflicting operations). Similarly, S11 is conflict equivalent to S12, and so on.
Note 1: Although S2 is not conflict serializable, still it is conflict equivalent to S21 and S21 because S2 can be converted to S21 and S22 by swapping non-conflicting operations.
Note 2: The schedule which is conflict serializable is always conflict equivalent to one of the serial schedule. S1 schedule discussed above (which is conflict serializable) is equivalent to the serial schedule (T1->T2).
Conflict Serializability in DBMS
As discussed in Concurrency control, serial schedules have less resource utilization and low throughput. To improve it, two or more transactions are run concurrently. However, concurrency of transactions may lead to inconsistency in the database. To avoid this, we need to check whether these concurrent schedules are serializable or not.