GATE CS 2021 Set 2 Q32 — Transactions and Concurrency Control

To evaluate the statements, let us analyze the schedule $S$ step-by-step:

1. Checking Statement $P$ (Conflict-Serializability):

We identify conflicting operations (different transactions, same data item, at least one write) to construct the precedence graph:

• On $X$: $W_1(X)$ occurs before $R_3(X)$, which gives the edge $T_1 \to T_3$.
• On $Y$: $R_1(Y)$ occurs before $W_2(Y)$, which gives the edge $T_1 \to T_2$.
• On $Z$: $R_2(Z)$ occurs before $W_3(Z)$, which gives the edge $T_2 \to T_3$.

The precedence graph contains the edges $T_1 \to T_2$, $T_1 \to T_3$, and $T_2 \to T_3$. Since there are no cycles in this graph, the schedule $S$ is conflict-serializable. Thus, $P$ is true.

2. Checking Statement $Q$ (Recoverability):

• There is a write-read dependency (dirty read) on data item $X$ because $T_3$ reads $X$ after it is written by $T_1$ ($W_1(X) \to R_3(X)$).
• For a schedule to be recoverable, any transaction $T_j$ that reads a value written by $T_i$ must commit only after $T_i$ commits.
• Therefore, $T_1$ must commit before $T_3$ commits.
• If $T_3$ commits before $T_1$ finishes, this condition is violated, making the schedule non-recoverable. Thus, $Q$ is false.

Hence, $P$ is true and $Q$ is false.