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

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

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