CS345 PROBLEM SET #5
SOLUTIONS
3 Questions, 100 pts.

Problem 1 (40 pts.)

student(S)

S is a student at Stanford.

office(S,O)

O is the office of S.

phone(S,P)

P is the phone of S.

major(S,M)

S is majoring in M.

advisor(S,A)

A is the advisor of S.

machine(S,M)

M is the machine of S.

group(S,G)

G is the group of S.

phone-dir(S,O,P) :- student(S) & office(S,O) & phone(S,P)

su-info(S,A,M) :- student(S) & advisor(S,A) & major(S,M)

acad-info(S,M,G) :- student(S) & major(S,M) & group(S,G)

cs-info(S,O,M) :- student(S) & major(S,cs) & office(S,O) & machine(S,M)

db-info(S,A,M,P) :- student(S) & major(S,cs) & group(S,db) & advisor(S,A) & machine(S,M) & phone(S,P).

a)

Express each of the following queries in terms of the global predicates.

• What are Andrew's phone number and office?
• What are Ben's office, machine, and advisor, given that he is a student in computer science?
• What are Cindy's major, advisor, and group?
• What are Debbie's advisor, office, and phone number, given that she is majoring in computer science and is a member of the database group?

b)

Find all minimal solutions (in terms of the available views) to each of the queries from a).

Solution

a)

answer1(P,O) :- student(a) & phone(a,P) & office(a,O)

answer2(O,M,A) :- student(b) & major(b,cs) & office(b,O) & machine(b,M) & advisor(b,A)

answer3(M,A,G) :- student(c) & major(c,M) & advisor(c,A) & group(c,G)

answer4(A,O,P) :- student(d) & major(d,cs) & group(d,db) & advisor(d,A) & office(d,O) & phone(d,P)

b)

answer1(P,O) :- phone-dir(a,O,P).

answer2(O,M,A) :- cs-info(b,O,M) & su-info(b,A,cs).

answer3(M,A,G) :- su-info(c,A,M) & acad-info(c,M,G).

answer4(A,O,P) :- phone-dir(d,O,P) & su-info(d,A,cs) & acad-info(d,cs,db).

Problem 2 (30 pts.)

phone-dir(S,O,P) - fff.

su-info(S,A,M) - bff.

acad-info(S,M,G) - bbf.

cs-info(S,O,M) - ffb or fbf.

db-info(S,A,M,P) - bfbf or bffb.

• Find all the students that have a given advisor.
• Find all students that share a given office.
• Find all computer science students.
• Find the group that a given machine belongs to.

Solution

query1_fb(S,A) :- phone-dir_fff(S,O,P) & su-info_bff(S,A,M).

query2_fb(S,O) :- phone-dir_fff(S,O,P).

query2_fb(S,O) :- cs-info_fbf(S,O,P).

query3_f(S) :- phone-dir_fff(S,O,P) & su-info_bff(S,A,cs).

query3_f(S) :- phone-dir_fff(S,O,P) & acad-info_bbf(S,cs,G).

query3_f(S) :- phone-dir_fff(S,O,P) & cs-info_fbf(S,O,M).

query4_fb(G,M) :- cs-info_ffb(S,O,M) & su-info_bff(S,A,N) & acad-info_bff(S,N,G)

Problem 3 (30 pts.)

Q1:

p(X) :- arc(X,Y) & arc(Y,Z) & arc(Z,X)

Q2:

p(X) :- arc(X,W) & arc(Y,W) & arc(W,Z) & arc(Z,Y) & arc(Z,X)

Q3:

p(X) :- arc(X,X1) & arc(X1,X2) & arc(X2,X3) & arc(X3,X4) & arc(X4,X5) & arc(X5,X)

Q4:

p(X) :- arc(X,Y) & arc(Y,X) & arc(X,Z).

a)

Minimize each query.

b)

Minimize their union.

Solution

a)

Q1:

p(X) :- arc(X,Y) & arc(Y,Z) & arc(Z,X) /* no change */.

Q2:

p(X) :- arc(X,W) & arc(W,Z) & arc(Z,X).

Q3:

p(X) :- arc(X,X1) & arc(X1,X2) & arc(X2,X3) & arc(X3,X4) & arc(X4,X5) & arc(X5,X) /* no change */.

Q4:

p(X) :- arc(X,Y) & arc(Y,X).

b)

Since Q1 and Q2 are equivalent and Q1 and Q4 are contained in Q3 then the minimized union of Q1, Q2, Q3, and Q4 is Q3.