The document discusses different types of schedules for transactions in a database including serial, serializable, and equivalent schedules. A serial schedule requires transactions to execute consecutively without interleaving, while a serializable schedule allows interleaving as long as the schedule is equivalent to a serial schedule. Equivalence is determined based on conflicts, views, or results between the schedules. Conflict serializable schedules can be tested for cycles in a precedence graph to determine if interleaving introduces conflicts, while view serializable schedules must produce the same reads and writes as a serial schedule.

2.  When multiple transactions are being executed by the
operating system in a multiprogramming environment,
there are possibilities that instructions of one transactions
are interleaved with some other transaction.

3. Schedule :
 A chronological execution sequence of a transaction is called a
schedule.
 A schedule can have many transactions in it, each comprising
of a number of instructions/tasks.
Serial schedule:
 A schedule S is serial if, for every transaction T participating in
the schedule, all the operations of T are executed consecutively
in the schedule.
 Otherwise, the schedule is called non serial schedule.
Serializable schedule:
• Serializable schedules are always considered to be correct
when concurrent transactions are executing.

4. 1. The main difference between the serial schedule and the
serializable schedule is that in serial schedule, no concurrency is
allowed whereas in serializable schedule, concurrency is
allowed.
2. In serial schedule, if there are two transaction executing at the
same time and if no interleaving of operations is permitted, then
there are only two possible outcomes :
 Execute all the operations of transaction T1 (in sequence) followed by all
the operations of transaction T2 (in sequence).
 Execute all the operations of transaction T2 (in sequence) followed by all
the operations of transaction T1 (in sequence).
In Serializable Schedule, if there are two transaction executing at
the same time and if interleaving of operations is allowed, there
will be many possible orders in which the system can execute the
individual operations of the transactions.

5. 3. In serializable schedule, the concurrent execution of schedule
should be equal to any serial schedule so that schedules are
always considered to be correct, when transaction executions
have interleaving of their operations in the schedules.

6.  Let T1 transfer $50 from A to B, and T2 transfer 10% of the balance
from A to B.
 A serial schedule in which T1 is followed by T2 :

7. • A serial schedule where T2 is followed by T1

8.  Let T1 and T2 be the transactions defined previously. The following
schedule is not a serial schedule, but it is equivalent to Schedule 1.
In Schedules 1, 2 and 3, the sum A + B is preserved.

9.  The following concurrent schedule does not preserve the
value of (A + B ).

10. When are 2 schedules equivalent?
There are three types of equivalence of schedules :
•Result equivalence
•Conflict equivalence
•View equivalence
Based on the types of equivalence, we define the types of
serializability. There are accordingly three types of serializability
which are:
•Conflict serializable
•View serializable
Result Equivalence :
In results equivalence, the end result of schedules heavily depend
on input of schedules. The final values are calculated from both
schedules (given and serial) and check whether they are equal.

11. Result Equivalence
NOT RESULT EQUIVALENCE

12.  Before we discuss conflict equivalence and conflict serializable
schedule, you must know about conflicts.
 What is a conflict?
 A pair of Operations in a schedule such that if their order is
interchanged then the behavior of at least one of the transactions
may change.
 Operations are conflict, if they satisfy all three of the following
conditions :
 They belong to different transactions
 They access the same data item
 At least one of the operation is a write operation.

15.  Schedules are conflict equivalent if they can be
transformed one into other by a sequence of non
conflicting interchanges adjacent actions.

17.  A Schedule is conflict serializable if it is conflict equivalent to
any of serial schedule.
Testing for conflict serializability
Method 1 :
 First write the given schedule in a linear way.
 Find the conflict pairs (RW, WR, WW) on same variable by
different transactions.
 Whenever conflict pairs are find, write the dependency relation
like Ti → Tj, if conflict pair is from Ti to Tj. For example,
(W1(A), R2(A)) ⇒ T1 → T2
 Check to see if there is a cycle formed,
 If yes= not conflict serializable
 No= we get a sequence and hence are conflict serializable.

20. Method 2:
 To test the conflict serializability, we can draw a Graph G = (V,E)
where
V = Vertices = number of transactions
E = Edges = for conflicting pair
Steps :
 Create node for each transaction.
 Find the conflict pairs (RW, WR, WW) on same variable by
different transactions.
 Draw edge from the schedule for each conflict pair such that for
example, W2(B), R1(A) is conflict pair, draw edge from T2 to T1
i.e. T2 must be executed before T1.
 Testing conditions for conflict serializability of schedule
 If precedence graph is cyclic non conflict serializable schedule
 If precedence graph is a acyclic conflict serializable schedule

21. W2(B)

22. W2(B)

23.  Let S and S´ be two schedules with the same set of transactions. S and S´ are
view equivalent if the following three conditions are met, for each data item
Q,
1. If in schedule S, transaction Ti reads the initial value of Q, then in
schedule S’ also transaction Ti must read the initial value of Q.
2. If in schedule S transaction Ti executes read(Q), and that value was
produced by transaction Tj (if any), then in schedule S’ also transaction
Ti must read the value of Q that was produced by the same write(Q)
operation of transaction Tj .
3. The transaction (if any) that performs the final write(Q) operation in
schedule S must also perform the final write(Q) operation in schedule S’.
As can be seen, view equivalence is also based purely on reads and writes alone.

24.  A schedule S is view serializable if it is view equivalent to a
serial schedule.
 Every conflict serializable schedule is also view serializable.
 Below is a schedule which is view-serializable but not conflict
serializable.
 What serial schedule is above equivalent to?
 Every view serializable schedule that is not conflict serializable
has blind writes.