Question

Q4.2 10 Points Suppose we have a set of transactions T1,..., Tn. Each transaction reads the same element X and writes back to X a value that is the result of multiplying X by some constant (eg X = X* 5). Each transaction may have a different constant, and for clarity you can call its constant Cn. Now consider a schedule of these transactions, S. which is serializable but not conflict-serializable nor serial. Describe S, and any assumptions you make about X, Tn, or Cn. Enter your answer here Why is your S serializable? Enter your answer here Why is your S not conflict-serializable? Enter your answer here Save Answer

Answer 1

A schedule S of transactions manipulating a data element X by multiplication with constants can be serializable if the final result is independent of transaction order due to the commutative property of multiplication. It is not conflict-serializable if rearranging the transactions leads to different intermediate states, indicating read-write or write-write conflicts.

Step-by-step explanation:

In this scenario, you have a set of transactions T1, ..., Tn where each transaction is performing an operation on a data element X, specifically multiplying X by a constant unique to that transaction (denoted as Cn). A schedule S of these transactions that is serializable but not conflict-serializable may involve operations that commute, meaning the order of transactions does not matter to the final result, but their interleaving cannot be converted into a schedule where the operations are strictly ordered without conflicting.

For example, suppose you have two transactions T1 and T2. T1 multiplies X by 2 (X = X * 2), and T2 multiplies X by 3 (X = X * 3). The final result of X after both transactions is the same regardless of the order they are applied since multiplication is commutative. However, this schedule could not be considered conflict-serializable because if you try to order these operations strictly (T1 before T2 or T2 before T1), the intermediate values of X will differ, which implies a read-write or write-write conflict.

The schedule S is serializable because it achieves the same final state as some serial execution of the transactions. It is not conflict-serializable because there is no way to reorder the transactions within S without encountering a conflict, as the operations are inherently non-conflicting only when applied in the specific non-serial order dictated by S.