Which of the following statements is false?

a$.$ Coordinator is a data processor $($DP$)$ node that participates in a distributed transaction using the two$-$phase COMMIT protocol.

b$.$ Two$-$phase commit protocol $(2$PC$)$ is an algorithm used to ensure atomicity of transactions and database consistency as well as integrity in distributed transactions.

c$.$ DO$-$UNDO$-$REDO protocol is used by a data processor $($DP$)$ to roll back or roll forward transactions with the help of a system's transaction log entries.

d$.$ Write$-$ahead protocol ensures transaction logs are written to permanent storage before any database data is actually updated.