Polynomial time algorithm - first order query, Mathematics

Assignment Help:

For queries Q1 and Q2, we say Q1 is contained in Q2, denoted Q1 ⊆ Q2, iff Q1 (D) ⊆ Q2(D) for every database D.

  • The container problem for a fixed Query Q0 is the following decision problem: Given a query Q, decide whether Q0 ⊆ Q.
  • The containee problem for a fixed query Q0 is the following decision problem: Given a query Q, decide whether Q ⊆ Q0.

Formally prove or disprove the following statements:

(a) For every conjunctive query Q0, there is a polynomial-time algorithm to decide the container problem for Q0 and for given conjunctive queries Q.

(b) For every conjunctive query Q0, there is a polynomial-time algorithm to decide the container problem for Q0 and for given conjunctive queries Q that can be obtained from Q0 by adding some atoms.

(c) For every conjunctive query Q0, there is a polynomial-time algorithm to decide the containee problem for Q0 and for given conjunctive queries Q.

(d) For every first-order Query Q0, there is an algorithm to decide the containee problem for Q0 and for given first-order queries Q. To prove a statement, sketch an algorithm, along with an argument why it is polynomial, if possible. To disprove it, provide an M-hardness or undecidability proof.


Related Discussions:- Polynomial time algorithm - first order query

Find the circumference of a circle, Find the circumference of a circle whos...

Find the circumference of a circle whose area is 16 times the area of the circle with diameter 7cm            (Ans: 88cm) Ans:     Π R 2 = 16 Π  r 2 R 2 = 16 r 2

Math, A small square is located inside a bigger square. The length of the s...

A small square is located inside a bigger square. The length of the small square is 3 in. The length of the large square is 7m. What is the area of the big square if you take out t

Apply depth-first-search to find out the spanning tree, Apply depth-first-s...

Apply depth-first-search to find out the spanning tree for the subsequent graph with vertex d as the starting vertex.        Ans: Let us begin with node'd'. Mark d as vi

Algorithm for division helping a child grasp, E1) Why don't you think of so...

E1) Why don't you think of some activities for the same purpose now? E2) Suggest, in detail, another activity for helping a child grasp the algorithm for division. We come to

Algebra, simplify mn+mp+nq+pq /n+p

simplify mn+mp+nq+pq /n+p

Determine the domain and range of function, Determine the domain of each of...

Determine the domain of each of the following functions.                         f( x ) = x - 4 / x 2 - 2 x -15 Solution With this problem we have to avoid division by

Prove that its inclination is given by cot = b cot - a, Two stations due...

Two stations due south of a leaning tower which leans towards the north are at distances a and b from its foot.  If α ,  β be the elevations of the top of the tower from these

Doubles Plus 1 and Doubles Minus 1, Write the doubles fact you used to solv...

Write the doubles fact you used to solve the problem. 7 + 8 = 15

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd