--%>
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 : What is the definition of a group Group

    Group: Let G be a set. When we say that o is a binary operation on G, we mean that o is a function from GxG into G. Informally, o takes pairs of elements of G as input and produces single elements of G as output. Examples are the operations + and x of

    		•
  • Q : Use MS Excel to do the computations

    Select a dataset of your interest (preferably related to your company/job), containing one variable and atleast 100 data points. [Example: Annual profit figures of 100 companies for the last financial year]. Once you select the data, you should compute 4-5 summary sta

    		•
  • 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 : Econ For every value of real GDP,

    For every value of real GDP, actual investment equals

    		•
  • Q : Global And Regional Economic Development

    The Pharmatec Group, a supplier of pharmaceutical equipment, systems and services, has its head office in London and primary production facilities in the US. The company also has a successful subsidiary in South Africa, which was established in 1990. Pharmatec South A

    		•
  • Q : Probability and Stochastic assignment

    Introduction to Probability and Stochastic Assignment 1: 1. Consider an experiment in which one of three boxes containing microchips is chosen at random and a microchip is randomly selected from the box.

    		•
  • Q : Budgeted cash disbursements The ABC

    The ABC Company, a merchandising firm, has budgeted its action for December according to the following information: • Sales at $560,000, all for cash. • The invoice cost for goods purc

    		•
  • Q : Who independently developed

    Who independently developed a model for simply pricing risky assets?

    		•
  • 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 Prime theory Suppose that p

    Suppose that p and q are different primes and n = pq. (i) Express p + q in terms of Ø(n) and n. (ii) Express p - q in terms of p + q and n. (iii) Expl

    		•