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

Real and distinct roots, Now we start solving constant linear, coefficient ...

Now we start solving constant linear, coefficient and second order differential and homogeneous equations. Thus, let's recap how we do this from the previous section. We start alon

RECTILINEAR FIGURES, AB,BC,CD ARE THREE CONSECUTIE SIDES OF REGULAR POLYGON...

AB,BC,CD ARE THREE CONSECUTIE SIDES OF REGULAR POLYGON.IF ANGLE BAC IS 18 DEGREE, FIND EXTERIOR ANGLES AND NUMBER OF SIDES ?

Subtraction involving negative numbers, Q. Subtraction Involving Negative N...

Q. Subtraction Involving Negative Numbers? In order to subtract positive and negative numbers, you need to be aware of the Rule for Subtraction. This rule states that subtracti

Evaluate following limits at infinity, Evaluate following limits. ...

Evaluate following limits. Solution In this part what we have to note (using Fact 2 above) is that in the limit the exponent of the exponential does this, Henc

Student, Patio measures 24 meters square. Patio stone are 30 cm each side. ...

Patio measures 24 meters square. Patio stone are 30 cm each side. How many stones are required to cover the patio?

Limit properties, Limit Properties :  The time has almost come for us t...

Limit Properties :  The time has almost come for us to in fact compute some limits.  Though, before we do that we will require some properties of limits which will make our lif

How does a child think-knowing your maths learner, HOW DOES A CHILD THINK? ...

HOW DOES A CHILD THINK? :  You must have interacted with children of various ages. From your experience, do you feel that children start learning, from a very early age, and conti

Problem solving, if you start a business and john creates 6 t shirts more t...

if you start a business and john creates 6 t shirts more than pedro and pedro four t shirts less than eva and between the three of then made 22 tshirts, how many t-shirts made each

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