CSE 233 Spring, 2012
Problem Set #1
Due on Tuesday , April 24
This is an individual assignment and the usual criteria for academic
integrity apply. Please typeset your answer (latex recommended). More
difficult problems are marked with ?.
1. The movie database consists of the following two relations
movie: title, director, actor
schedule: theater, title
The first relation provides titles, directors, and actors of various movies.
Assume a movie is uniquely identified by its title. Do not assume that
a movie has a unique director (so a movie by Hitchcock is one for which
one of the directors is Hitchcock). The second relation provides the titles
of currently playing movies and the theaters where they are being shown.
Express the following queries in (i) relational calculus, (ii) relational algebra
and (iii) nr-Datalog¬.
(a) List the theaters showing some movie by Hitchcock.
(b) List the theaters showing only movies by Hitchcock.
2. The division binary operator ÷on relations is defined as follows. Given
relations Pand Qfor which att(Q)⊂att(P), P÷Qis a relation with
attributes att(P)−att(Q) containing the tuples tfor which {t}1Q⊆P.
For example, if att(P) = {A, B}and att(Q) = {B},P÷Qis the relation with
attribute {A}containing the tuples haifor which ha, bi ∈ Pfor every tuple
hbi ∈ Q. Intuitively, ÷is a direct implementation of universal quantification.
(i) Use ÷(and standard algebra operators) to express the query “List the
theaters showing every movie by Hitchcock”.
(ii) Show how P÷Qcan be expressed using the standard relational algebra
operators (you can assume, for simplicity, that att(P) = {A, B}and
att(Q) = {B}).
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