Prove that with a two-phase locking protocol, one possible equivalent serial order is the order in which the transactions perform their first unlock operation.
What will be an ideal response?
If two transactions do not acquire conflicting locks in some schedule S, all their
operations commute and they can be ordered arbitrarily in an equivalent serial schedule. Suppose they acquire conflicting locks on item x, and T1 accesses x before T2. Then
T1’s first unlock in S must precede T2’s lock on x, which must precede T2’s first
unlock. If they also acquire conflicting locks on y, their accesses to y must be in the
same order as their accesses to x since otherwise we could conclude that T2’s first
unlock in S must precede T1’s first unlock – a contradiction. Hence, all conflicting
operations in T1 and T2 are ordered in the same way as their first unlock events and
the two transactions can be serialized in that order.
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