CSE 233 Spring, 2012
Problem Set #5
Due on Thursday, June 7
1. (5 points) Consider the schema consisting of a unary relation Nand two
binary relations C1and C2. Consider the set Bof binary trees represented
by this schema as follows: Nprovides the set of nodes, C1(a, b) means that
bis the first child of a, and C2(a, b) means that bis the second child of a
(each node has zero or two children). Show that fixpoint expresses all ptime
queries over the set of binary trees Brepresented as above.
2. (5 points) In this problem we consider Datalog programs with no con-
stants or (in)equality. We say that a graph property is definable by a Datalog
program Pwith some designated IDB relation answer and one binary EDB
relation Giff for every G,answer is non-empty in P(G) iff the property
holds for G. Show the following:
(i) (3 points) The existence of a path of even length between two desig-
nated nodes aand bin a graph is definable in Datalog.
(ii) (2 points) The existence of a simple path of even length between two
designated nodes aand bin a graph is not definable in Datalog.
3. (4points) Recall that inclusion of Datalog programs is undecidable. Show
that it is decidable, for a conjunctive query Ļand a Datalog program P,
whether ĻāP(i.e., Ļ(I)āP(I) for every input I).
4. (6points) Consider the movie database consisting of two relations Schedule[theater,
title] and Movie[title, director, actor]. We do not make the unique director
assumption, so one title may have multiple directors. Consider the query
āList the theaters showing only movies by Hitchcockā.
(i) (3points) Express the query in DatalogĀ¬with inflationary fixpoint
semantics.
(ii) (3points) Suppose that in addition to the above relations, the database
provides for each attribute Aā {theater,titl e, actor}a relation succA
providing a successor relation on the set of values of attribute Ain
the database. In addition, assume minAand maxAare constants
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