Task $1(2$ marks$)$

Concurrent processing of database transactions

$(2)(1$ mark$)$

Consider the database transactions listed below.

T $1$

$a=$read$(x)$

$b=$read$(y)$

write $(z,a+b)$

commit

T$2$

$a=$ read $(x)$

write $(y,a+1)$

commit

$T3$

$c=$read$(x)$

write $(x,c+1)$

write $(z,c+2)$

commit

Assume that the initial values of the persistent data items $x,y$ and $z$ are the following: $x=2,y=0$ and $z=2.$

Show a sample concurrent execution of the transactions T$1,$ T$2,$ and T$3$ that is NOT conflict serializable.

Prove that the execution is NOT conflict serializable.

To prove that the execution is NOT conflict serializable use a technique of two$-$dimensional diagrams presented to you during the lecture classes, for example, see a presentation $10$ Introduction to Transaction Processing $(1),$ slide $9.$