Question 61

The protocol specifies:

1. Step 1: Transaction $T$ acquires exclusive locks on objects $\{O_1, \dots, O_k\}$ in increasing order of their addresses.
2. Step 2: The required operations are performed.
3. Step 3: All locks are released.

1. Serializability:

• All locks are acquired before any lock is released (in fact, this is strict conservative 2PL).
• Because every transaction follows a two-phase locking rule (a growing phase where locks are acquired, followed by a shrinking phase where locks are released), the conflict serializability of any schedule under this protocol is guaranteed.

2. Deadlock Freedom:

• Deadlock requires four Coffman conditions: Mutual Exclusion, Hold and Wait, No Preemption, and Circular Wait.
• In this protocol, objects are linearly ordered by their memory addresses.
• Every transaction must request exclusive locks strictly according to this global increasing order.
• According to Havender's linear ordering principle, a circular wait condition is mathematically impossible because any cycle $T_1 \to T_2 \to \dots \to T_m \to T_1$ would imply an impossible strict inequality in object addresses: $\text{addr}(O_{i_1}) < \text{addr}(O_{i_2}) < \dots < \text{addr}(O_{i_1})$.
• Therefore, the protocol guarantees deadlock freedom.

Thus, the protocol guarantees both serializability and deadlock-freedom (Option A).