Homework Help is Here – Start Your Trial Now!
Engineering
Computer Science
In the k-XOR problem, we are given n boolean variables x₁,x2,..., xn, a list of m clauses each of which is the XOR of exactly k distinct variables (that is, the clause is true if and only if an odd number of the k variables in the clause are true), and an integer r. Our goal is to decide if there is some assignment of variables that satisfies at least r clauses. (a) In the Max-Cut problem, we are given an undirected unweighted graph G = (V, E) and integer c and want to find a cut SC V such that at least c edges cross this cut (i.e. have exactly one endpoint in S). Give and argue correctness of a reduction from Max-Cut to 2-XOR. Hint: every clause in 2-XOR is equivalent to an edge in Max-Cut. (b) Give and argue correctness of a reduction from 3-XOR to 4-XOR.

In the k-XOR problem, we are given n boolean variables x₁,x2,..., xn, a list of m clauses each of which is the XOR of exactly k distinct variables (that is, the clause is true if and only if an odd number of the k variables in the clause are true), and an integer r. Our goal is to decide if there is some assignment of variables that satisfies at least r clauses. (a) In the Max-Cut problem, we are given an undirected unweighted graph G = (V, E) and integer c and want to find a cut SC V such that at least c edges cross this cut (i.e. have exactly one endpoint in S). Give and argue correctness of a reduction from Max-Cut to 2-XOR. Hint: every clause in 2-XOR is equivalent to an edge in Max-Cut. (b) Give and argue correctness of a reduction from 3-XOR to 4-XOR.

Database System Concepts
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
See similar textbooks
icon
Related questions
Question

Alert dont submit AI generated answer.

In the k-XOR problem, we are given n boolean variables x1, x2, ..., n, a list of m clauses each of which is the XOR of exactly k distinct variables (that is, the clause is true if and only if an odd number of the k variables in the clause are true), and an integer r. Our goal is to decide if there is some assignment of variables that satisfies at least r clauses. (a) In the Max-Cut problem, we are given an undirected unweighted graph G = (V, E) and integer c and want to find a cut SC V such that at least c edges cross this cut (i.e. have exactly one endpoint in S). Give and argue correctness of a reduction from Max-Cut to 2-XOR. Hint: every clause in 2-XOR is equivalent to an edge in Max-Cut. (b) Give and argue correctness of a reduction from 3-XOR to 4-XOR.
Transcribed Image Text:In the k-XOR problem, we are given n boolean variables x1, x2, ..., n, a list of m clauses each of which is the XOR of exactly k distinct variables (that is, the clause is true if and only if an odd number of the k variables in the clause are true), and an integer r. Our goal is to decide if there is some assignment of variables that satisfies at least r clauses. (a) In the Max-Cut problem, we are given an undirected unweighted graph G = (V, E) and integer c and want to find a cut SC V such that at least c edges cross this cut (i.e. have exactly one endpoint in S). Give and argue correctness of a reduction from Max-Cut to 2-XOR. Hint: every clause in 2-XOR is equivalent to an edge in Max-Cut. (b) Give and argue correctness of a reduction from 3-XOR to 4-XOR.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Minimum and Maximum
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.
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
SEE MORE TEXTBOOKS