# Relational vs. PICK/Object DBMS

From: x <x-false_at_yahoo.com>

Date: Wed, 21 Apr 2004 10:04:13 +0300

Message-ID: <40861c4a$1_at_post.usenet.com>

Date: Wed, 21 Apr 2004 10:04:13 +0300

Message-ID: <40861c4a$1_at_post.usenet.com>

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Sorry for the omissions/errors in the previous post.

1)Been given the domains {A,A1,A2,...,An}, with large n and the following database schema:

- for all i in 1..n, Ri(A,Ai) is a base relation
- for all i in 1..n, A is a candidate key for the relation Ri

answer the questions:

- for {i1,i2,...,ip} given , find R(A,Ai1,Ai2,...,Aip) with the constraints R(A,Aik) = Rik(A,Aik) for all k in 1..p, R is minimal.
- for a in A given, find R(A,Ai1,Ai2,...,Aip) with the constraints:
- R(A=a,Aik) = Rik(A=a,Aik) for all k in 1..p
- {Ai1,...,Aip} is maximal
- R is minimal

- Let P(A) be the power set of domain A for any domain A.
Been given the domains {A,B,C} and the database schema
R1(P(A),P(B)), R2(P(B),P(C))
answer the question:
find R(P(A),P(B),P(C)) with the contstraints:
- R(P(A),P(B))=R1(P(A),P(B))
- R(P(B),P(C))=R2(P(B),P(C))
- R minimal

Note:

- No NULLs are allowed
- R(X1,X2,...,Xp) is the projection of R on the attributes (X1,...,Xp)
- R(X1=a,X2,...,Xp) is the projection of R on the attributes (X1,...,Xp) followed by the selection upon X1=a (or viceversa)
- R1(P(A1),P(A2), ..., P(Ap))=R2(P(A1),P(A2),...,P(Ap)) iff
- for any (X1,...,Xp) in R1, for any (x1,...,xp) in X1xX2,...xXp there is an (Y1,...,Yp) in R2 such that (x1,...,xp) is in Y1xY2x...xYp
- for any (Y1,...,Yp) in R2, for any (y1,...,yp) in Y1xY2,...xYp there is an (X1,...,Xp) in R1 such that (y1,...,yp) is in X1xX2x...xXp

- for any R(P(A1),P(A2),...,P(Ap)), for any two distinct (X1,X2,...,Xp) , (Y1,Y2,...,Yp) from R, X1x...xXp /\ Y1x...xYp is void where /\ stands for intersection and x for cartesian product.
- A maximal (minimal) means A has a maximal (minimal) number of elements.

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