GATE CS 2025 Set 1 Q5 — Transactions and Concurrency Control

To determine which transactions must be rolled back when $T_1$ aborts, we need to identify any dirty reads (reading uncommitted data written by an active transaction).

Let's analyze the sequence of operations in the given schedule:

1. $R_1(X)$: $T_1$ reads $X$.
2. $W_1(Y)$: $T_1$ writes to $Y$.
3. $R_2(X)$: $T_2$ reads $X$.
4. $R_2(Y)$: $T_2$ reads $Y$. Since $T_1$ has written $Y$ but has not committed yet, this is a dirty read. $T_2$ is now dependent on $T_1$.
5. $R_3(Y)$: $T_3$ reads $Y$. This is also a dirty read of the uncommitted value written by $T_1$. $T_3$ is now dependent on $T_1$.
6. $\operatorname{ABORT}(T_1)$: $T_1$ aborts.

Because $T_1$ aborts, any transaction that read uncommitted data written by $T_1$ must also be rolled back to prevent cascading inconsistency (cascading rollback).

• Since $T_2$ read $Y$ from $T_1$, $T_2$ must be rolled back.
• Since $T_3$ read $Y$ from $T_1$, $T_3$ must be rolled back.

Therefore, both $T_2$ and $T_3$ are required to be rolled back.