3. Transaction Processing

Consider schedules S1 and S2 below.

S1: r2(X), r2(Z), r3(Y), w2(X), w2(Z), w3(Y), r1(Z), r3(X), w3(X), r1(X), r3(Z), w1(X), w3(Z), w1(Z)
S2: r1(X), r1(Z), r2(Y), w2(Y), w1(X), r3(Y), w1(Z), r2(X), r3(X), r2(Z), w2(Z), r3(Z), w3(Y), w3(Z)

(a) Apply the basic timestamp ordering (BTO) algorithm to schedules S1 and S2. Determine whether or not the
algorithm allows the execution of the schedules, and discuss cascading rollback (if any).
Hints: each operation takes one-time unit, and timestamp of each transaction is the time associated to its first operation.
For example, timestamps of transactions T1, T2, and T3 in schedule S1 are 7, 1, and 3 (respectively). [20 marks]

(b) Testing the serializability of S1 and S2 by serialization graph technique to prove that the successful execution of a
schedule under BTO will ensure the serializability of the schedule. [15 marks]

(c) Examine the recoverable characteristic of S1 and S2 and check if the schedules are cascadeless and/or strict
schedules. Write an equivalent strict schedule if they are cascadeless and not a strict schedule. We assume that a
transaction will be committed or aborted right after its last operation. [15 marks]

4. Deductive Database

Consider a deductive database with the following rules:
ANCESTOR(X, Y) :- PARENT(X, Y)
ANCESTOR(X, Y) :- PARENT(X, Z), ANCESTOR(Z, Y)

Notice that PARENT(X, Y) means that X, Y are human-beings and Y is the (biological) parent of X; ANCESTOR(X, Y) means
that Y is the ancestor of X.

Consider the following fact base:
PARENT(john, steve), PARENT(john, olivia), PARENT(olivia, emma), PARENT(olivia, william).

(a) Construct either a model theoretic interpretation or a proof theoretic interpretation of the above rules using the
given facts. [10 marks]


Consider that a database contains the following relations PARENT(X, Y), and a relation BIRTH(X, B), where B is the birth
date of a person X.

The following information is used for question (b), (c) and (d).
Assume that we have the following family tree:
emma william

martin olivia steve
tony john

jenny david michael dorothy

sophia christopher
PARENT(olivia, william).
PARENT(olivia, emma).
PARENT (tony, martin).
PARENT (tony,olivia).
PARENT (john, olivia).
PARENT (john, steve).
PARENT (jenny, tony).
PARENT (david, tony).
PARENT (michael, john).
PARENT (dorothy, john).
PARENT (sophia, jenny).
PARENT (christopher, michael).

(b) State a new rule named as SIBLING(X, Y) and construct a proof theoretic interpretation of this rule to find all siblings .
[10 marks]

(c) State a new rule named as DESCENDANT(X, Y) and construct a proof theoretic interpretation of this rule to find all
descendants of Martin. Note DESCENDANT(X, Y) means Y is a descendant of X. [10 marks]

(d)
Given the following rules:

FIRST_COUSIN(X, Y) :- PARENT(X, Z), PARENT(Y, T), SIBLING(Z, T)
COUSIN(X, Y) :- FIRST_COUSINS(X, Y)
COUSIN(X, Y) :- PARENT(X, Z), PARENT(Y, T), COUSIN(Z, T)

Note: Two people are first cousins if their parents are siblings. Cousins means any kind of cousins. Cousins can be
second cousins who are the children of the two first cousins or third cousins who are the children of two second cousins
etc.

1. Prove that FIRST_COUSIN(jenny, michael) is true. [10 marks]

2. Prove that COUSIN(sophia, christopher) is true. [10 marks]
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