--%>
Assignment Help - homework help

Containee problem

For queries Q1 and Q2, we say Q1 is containedin Q2, denoted Q1 C Q2, iff Q1(D) C Q2(D) for every database D.

The container problern for a fixed Query Qo is the following decision problem:
Given a query Q, decide whether Qo C Q.

The containee probletn for a fixed guery Qo is the following decision problem:
Given a query Q, decide whether Q C Qo.

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 Qo by adding some atoms.

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

(d) For every flrst-order Query Q0, there is an algorithm to decide the containee problem for Qo 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 Questions in Mathematics

  • Q : Explain Factorisation by trial division

    Factorisation by trial division: The essential idea of factorisation by trial division is straightforward. Let n be a positive integer. We know that n is either prime or has a prime divisor less than or equal to √n. Therefore, if we divide n in

    		•
  • Q : How do it? integral e^(-t)*e^(tz) t

    integral e^(-t)*e^(tz) t between 0 and infinity for Re(z)<1

    		•
  • Q : Law of iterated expectations for

     Prove the law of iterated expectations for continuous random variables. 2. Prove that the bounds in Chebyshev's theorem cannot be improved upon. I.e., provide a distribution that satisfies the bounds exactly for k ≥1, show that it satisfies the bounds exactly, and draw its PDF. T

    		•
  • Q : Theorem-Group is unique and has unique

    Let (G; o) be a group. Then the identity of the group is unique and each element of the group has a unique inverse.In this proof, we will argue completely formally, including all the parentheses and all the occurrences of the group operation o. As we proce

    		•
  • Q : Explain the work and model proposed by

    Explain the work and model proposed by Richardson.

    		•
  • Q : Problem on Fermats method A public key

    A public key for RSA is published as n = 17947 and a = 3. (i) Use Fermat’s method to factor n. (ii) Check that this defines a valid system and find the private key X.

    Q : Problem on mass balance law Using the

    Using the mass balance law approach, write down a set of word equations to model the transport of lead concentration. A) Draw a compartmental model to represent  the diffusion of lead through the lungs and the bloodstream.

    		•
  • Q : Formulating linear program of an oil

    An oil company blends two input streams of crude oil products alkylate and catalytic cracked to meet demand for weekly contracts for regular (12,000 barrels) mind grade ( 7,500) and premium ( 4,500 barrels) gasoline’s . each week they can purchase up to 15, 000

    		•
  • Q : Properties for polynomial Specify the

    Specify the important properties for the polynomial.

    		•
  • Q : State Measuring complexity Measuring

    Measuring complexity: Many algorithms have an integer n, or two integers m and n, as input - e.g., addition, multiplication, exponentiation, factorisation and primality testing. When we want to describe or analyse the `easiness' or `hardness' of the a

    		•