Problem 7. Define the language:ODD3SAT = {4: p is a 3CNF formula over n variables and has a satisf ying assignmentin which every clause has an odd number of TRUE literals.}Prove that ODD3SAT e P.To get started, instead of a boolean variable that is either TRUE or FALSE, think of x¡ as either 1 or 0.A. How would you replace the logical expressions x, and x¡ V x¡ by equivalent arithmeticexpressions modulo 2?B. Describe how to convert each clause of o into a linear equation modulo 2, so that a truthassignment satisfies the clause if and only if the corresponding numerical values of the literalssatisfy the equation.C. Describe how to convert the conjunction of clauses of into a system of linear equations suchthat a truth assignment satisfies ø if and only if the corresponding numerical valuessimultaneously satisfy all the linear equations.D. Describe a polynomial time algorithm to solve the system of linear equations.

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Answered: ODD3SAT = {4: is a 3CNF formula over n…

ODD3SAT = {4: is a 3CNF formula over n variables and has a satisf ying assignment in which every clause has an odd number of TRUE literals.} Prove that ODD3SAT e P.

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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Question

Problem 7. Define the language:
ODD3SAT = {4: p is a 3CNF formula over n variables and has a satisf ying assignment
in which every clause has an odd number of TRUE literals.}
Prove that ODD3SAT e P.
To get started, instead of a boolean variable that is either TRUE or FALSE, think of x¡ as either 1 or 0.
A. How would you replace the logical expressions x, and x¡ V x¡ by equivalent arithmetic
expressions modulo 2?
B. Describe how to convert each clause of o into a linear equation modulo 2, so that a truth
assignment satisfies the clause if and only if the corresponding numerical values of the literals
satisfy the equation.
C. Describe how to convert the conjunction of clauses of into a system of linear equations such
that a truth assignment satisfies ø if and only if the corresponding numerical values
simultaneously satisfy all the linear equations.
D. Describe a polynomial time algorithm to solve the system of linear equations.

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