Given boolean formula in conjunctive normal form with M clauses and N literals such that each clause has exactly two literals, find a satisfying assignment (if one exists). Hint : Form the implication digraph with 2N vertices (one per literal and its negation). For each clause x + y, include edges from y' to x and from x' to y. To satisfy the clause x + y, (i) if y is false, then x is true and (ii) if x is false, then y is true. Claim: The formula is satisfiable if and only if no variable x is in the same strong component as its negation x'. Moreover, a topological sort of the kernel DAG (contract each strong component to a single vertex) yields a satisfying assignment.
Given boolean formula in conjunctive normal form with M clauses and N literals such that each clause has exactly two literals, find a satisfying assignment (if one exists). Hint : Form the implication digraph with 2N vertices (one per literal and its negation). For each clause x + y, include edges from y' to x and from x' to y. To satisfy the clause x + y, (i) if y is false, then x is true and (ii) if x is false, then y is true. Claim: The formula is satisfiable if and only if no variable x is in the same strong component as its negation x'. Moreover, a topological sort of the kernel DAG (contract each strong component to a single vertex) yields a satisfying assignment.
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
Related questions
Question
100%
Given boolean formula in conjunctive normal form with M clauses and N literals such that each clause has exactly two literals, find a satisfying assignment (if one exists). Hint : Form the implication digraph with 2N vertices (one per literal and its negation). For each clause x + y, include edges from y' to x and from x' to y. To satisfy the clause x + y, (i) if y is false, then x is true and (ii) if x is false, then y is true. Claim: The formula is satisfiable if and only if no variable x is in the same strong component as its negation x'. Moreover, a topological sort of the kernel DAG (contract each strong component to a single vertex) yields a satisfying assignment.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Knowledge Booster
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
Recommended textbooks for you
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)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
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)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education