Reference no: EM132314256

Advanced Databases and Applications Assignment -

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).

(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.

(c) Examine the recoverable characteristic of S₁ and S₂. What schedule (S1 or S2) can be executed under the strict timestamp ordering (STO) algorithm and write an equivalent strict schedule for it? We assume that a transaction will be be committed or aborted right after its last operation.

(d) Examine the two-phase locking (2PL) technique on S₁ and S₂ with an assumption of unlock operations being done as late as possible. Are BTO schedules also 2PL schedules?

Deductive Database -

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 a model theoretic interpretation of the above rules using the given facts.

The following information is used for question (b), (c) and (d).

Consider that a database contains the following relations PARENT(X, Y).

Assume that we have the following family tree:

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

(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.

(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.

2. Prove that COUSIN(sophia, christopher) is true.