Given a boolean formula in conjunctive normal form with M clauses and N literals, find a satisfying assignment (if one exists), such that each clause has precisely two literals. With 2N vertices (one for each literal and its negation), create an implication digraph. For each phrase x + y, take into account the edges from y' to x and x' to y. In order to fulfil the condition x + y, both (i) x must be true if y is false and (ii) y must be true if x is false. If and only if no variable x is in the same strong component as its negation x', the formula is true. Additionally, a topological sort of the kernel DAG (which reduces each strong component to a single vertex) results in an assignment that is adequate.
Given a boolean formula in conjunctive normal form with M clauses and N literals, find a satisfying assignment (if one exists), such that each clause has precisely two literals. With 2N vertices (one for each literal and its negation), create an implication digraph. For each phrase x + y, take into account the edges from y' to x and x' to y. In order to fulfil the condition x + y, both (i) x must be true if y is false and (ii) y must be true if x is false. If and only if no variable x is in the same strong component as its negation x', the formula is true. Additionally, a topological sort of the kernel DAG (which reduces each strong component to a single vertex) results in an assignment that is adequate.
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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Given a boolean formula in conjunctive normal form with M clauses and N literals, find a satisfying assignment (if one exists), such that each clause has precisely two literals. With 2N vertices (one for each literal and its negation), create an implication digraph. For each phrase x + y, take into account the edges from y' to x and x' to y. In order to fulfil the condition x + y, both (i) x must be true if y is false and (ii) y must be true if x is false. If and only if no variable x is in the same strong component as its negation x', the formula is true. Additionally, a topological sort of the kernel DAG (which reduces each strong component to a single vertex) results in an assignment that is adequate.
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