Question $6$: Transactions $(15$ marks$)$

Let transactions $T1,T2$ and $T3$ be defined to perform the following operations:

T$1$: Add one to $A$

T$2$: Double $A$

T$3$: Display the current value of $A$ on the screen and then set $A$ to one

$($where $A$ is some numeric item in the database$).$

$($a$)$ Suppose transactions T$1,$ T$2$ and T$3$ are allowed to execute concurrently. If A has

initial value zero, how many possible correct results are there? List them.

$($b$)$ Suppose the internal structure of T$1,$ T$2$ and T$3$ is as indicated in the following

pseudocode. If A has initial value zero, is there any interleaved schedules that in

fact product a correct result and yet is not serializable? Explain your answer.

Question $6($continued$)$

$($c$)$ Are there any schedules that are in fact serializable but could not be produced if

all three transactions obeyed the two$-$phase locking protocol? Show your work.