Question

1. Consider the following schedule S TI T2 read(A) write(A write(A) write(A (a) Draw the precedence graph of S (b) Is schedule S serializable? If so, name one equivalent serial schedule, and prove equivalence (c) Denote by S"the schedule obtained by replacing the write(A) in T2 with read(A) in S. Is schedule S" serializable? If so, name one equivalent serial schedule and prove equivalence. Otherwise prove that it is not. (d) Denote by S"the schedule obtained by replacing the write(A) in T3 with read(A) in S. Is schedule S" serializable? If so, name one equivalent serial schedule, and prove equivalence. Otherwise prove that it is not.

Answer 1

a)

T1 T2 T3

b) Since there is a cycle in the above precedence graph of S, S is not serializable.

c) Below is the precendence graph pf S'.

Since there is no cycle in the above graph, S' is serializable.

A schedule is equivalent to other is the effect of executing first schedule is same as executing the other.

Equivalent schedule of S'(Se): T2 - T1 - T3

The two schedules are equivalent because:

1. T2 reads initial value of A in both S' and Se.
2. T1 reads initial value of A in both S' and Se.
3. T3 writes final value of A written by T1 in both S' and S''.

d) The precendence graph for S'' is same as S, hence it is not serializable as it has a cycle.