--%>
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 : Graph Theory is the n-Dimensional Qn

    is the n-Dimensional Qn Hamiltonian? Prove tour answer

    		•
  • Q : Problem on Linear equations Anny, Betti

    Anny, Betti and Karol went to their local produce store to bpought some fruit. Anny bought 1 pound of apples and 2 pounds of bananas and paid $2.11.  Betti bought 2 pounds of apples and 1 pound of grapes and paid $4.06.  Karol bought 1 pound of bananas and 2

    		•
  • 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 : What is Big-O hierarchy The big-O

    The big-O hierarchy: A few basic facts about the big-O behaviour of some familiar functions are very important. Let p(n) be a polynomial in n (of any degree). Then logbn is O(p(n)) and p(n) is O(an<

    		•
  • Q : Set Theory & Model of a Boolean Algebra

    II. Prove that Set Theory is a Model of a Boolean Algebra The three Boolean operations of Set Theory are the three set operations of union (U), intersection (upside down U), and complement ~.  Addition is set

    		•
  • Q : Probability assignments 1. Smith keeps

    1. Smith keeps track of poor work. Often on afternoon it is 5%. If he checks 300 of 7500 instruments what is probability he will find less than 20substandard? 2. Realtors estimate that 23% of homes purchased in 2004 were considered investment properties. If a sample of 800 homes sold in 2

    		•
  • Q : Explain Factorisation by Fermats method

    Factorisation by Fermat's method: This method, dating from 1643, depends on a simple and standard algebraic identity. Fermat's observation is that if we wish to nd two factors of n, it is enough if we can express n as the di fference of two squares.

    		•
  • Q : Formulating linear program of a

    A software company has a new product specifically designed for the lumber industry. The VP of marketing has been given a budget of $1,35,00to market the product over the quarter. She has decided that $35,000 of the budget will be spent promoting the product at the nat

    		•
  • Q : Numerical solution of PDE this

    this assignment contains two parts theoretical and coding the code has to be a new. old code and modified code will appear in the university website .

    		•
  • Q : Breakfast program if the average is

    if the average is 0.27 and we have $500 how much break fastest will we serve by 2 weeks

    		•