Answered: Given boolean formula in conjunctive…

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 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.

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