EBK DATA STRUCTURES AND ALGORITHMS IN C
4th Edition
ISBN: 9781285415017
Author: DROZDEK
Publisher: YUZU
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Chapter 2, Problem 13E
Program Plan Intro
Satisfiability Problem:
The problem to determine if there exists an interpretation that would satify a given boolean formula is known a satisfiability problem.
- In a given Boolean formula it is asked whether it’s variables could be replaced by values “TRUE” or “FALSE” such that formula evaluates to “TRUE”.
- In such a case, the boolean formula is called satisfiable.
- Otherwise, if there is no such assignment possible and the function becomes “FALSE” for all variable assignments possible, then the formula is unsatisfiable.
3-Satisfiablity:
The satisfiability of a formula stated in a conjunctive normal (CNF) form is been determined where each clause is been limited to atmost three literals, such a problem is termed as 3-satisfiability problem.
Explanation of Solution
Boolean expression with one variables:
Consider an instance when an alternative in a Boolean expression has two variables.
Convert the above satisfiablity problem into 3-satisfiability problem by generating the below expression. Transform each clause into a conjunction of “n-2” clauses, where “n” denotes the total count of literals in all clauses.
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EBK DATA STRUCTURES AND ALGORITHMS IN C
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