opose that we have three variables X1, X2 and X3, which are defined on the same domain of 2,3}. Two binary constraints for these three variables are defined as follows: SR12 {(X1, X2),[(2, 1), (2,3), (3, 2), (3,3)]} R13 {(X1, X3), [(1,2), (2, 1), (3, 1), (3,3)|} %3D (12 points) Is X1 arc-consistent with respect to X2? And is X1 arc-consistent with respect to X3? and why? In addition, is X3 arc-consistent with respect X1 if the constraints between R and R3 are undirected (i.e., R31 is defined as {(X3, X1), [(2, 1), (1, 2), (1,3), (3,3)]} that switches the clement order of every two-tuple of R13)? and why? (12 points) Suppose that, after some inference, the domain of X1 is reduced as (2,3} and the constrains in R12 and R13 for X1 is removed from R13 due to reducing the domain of X1. Now is X1 still arc-consistent with = 1 are removed accordingly. To be more specific, (1,2)

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
icon
Related questions
Question
Suppose that we have three variables X1, X2 and X3, which are defined on the same domain of
{1,2, 3}. Two binary constraints for these three variables are defined as follows:
R12 = {(X1, X2), [(2, 1), (2,3), (3, 2), (3,3)]}
R13 = {(X1, X3), [(1,2), (2, 1), (3, 1), (3,3)]}
1. (12 points) Is X1 arc-consistent with respect to X2? And is X1 arc-consistent with respect
to X3? and why? In addition, is X3 arc-consistent with respect X1 if the constraints between
Rị and R3 are undirected (i.e., R31 is defined as {(X3, X1), [(2, 1), (1, 2), (1,3), (3,3)]} that
switches the clement order of every two-tuple of R13)? and why?
2. (12 points) Suppose that, after some inference, the domain of Xı is reduced as {2, 3} and the
constrains in R12 and R13 for X1 = 1 are removed accordingly. To be more specific, (1,2)
is removed from R13 due to reducing the domain of X1. Now is X1 still arc-consistent with
respect to X2? And is X1 arc-consistent with respect to X3? and why? In addition, is X3 still
arc-consistent with respect X1 if the constraints between R1 and R3 are undirected? and why?
Transcribed Image Text:Suppose that we have three variables X1, X2 and X3, which are defined on the same domain of {1,2, 3}. Two binary constraints for these three variables are defined as follows: R12 = {(X1, X2), [(2, 1), (2,3), (3, 2), (3,3)]} R13 = {(X1, X3), [(1,2), (2, 1), (3, 1), (3,3)]} 1. (12 points) Is X1 arc-consistent with respect to X2? And is X1 arc-consistent with respect to X3? and why? In addition, is X3 arc-consistent with respect X1 if the constraints between Rị and R3 are undirected (i.e., R31 is defined as {(X3, X1), [(2, 1), (1, 2), (1,3), (3,3)]} that switches the clement order of every two-tuple of R13)? and why? 2. (12 points) Suppose that, after some inference, the domain of Xı is reduced as {2, 3} and the constrains in R12 and R13 for X1 = 1 are removed accordingly. To be more specific, (1,2) is removed from R13 due to reducing the domain of X1. Now is X1 still arc-consistent with respect to X2? And is X1 arc-consistent with respect to X3? and why? In addition, is X3 still arc-consistent with respect X1 if the constraints between R1 and R3 are undirected? and why?
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Uncertainty Problems
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education