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In Boolean logic, a sentence is S = C¡ ^ C2 ^ C3 ^ …· ^ three literals.

In Boolean logic, a sentence is S = C¡ ^ C2 ^ C3 ^ …· ^ three literals.

Database System Concepts
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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In Boolean logic, a sentence is in 3-Conjunctive Normal Form (abbreviated 3-CNF) if it of the form C1 ^ C2 ^ C3 ^ .…. A Cm, where S is the conjunction of m clauses, with each clause being a disjunction of S three literals. We say that S is satisfiable if there exists an assignment of TRUE/FALSE values to each variable so that the entire sentence S evaluates to TRUE. For example, in the last class, we showed that the following 3-CNF sentence, with m=8 clauses, is not satisfiable. D) ^ (B v č v D) ^ (c vĀ v D) ^ (A (A v (Bv č v D) A (c v Ā v D) a (A v B V C) ^ (a v B v C) A V v B v D) S = AVВV A V B Let 3-SAT be the decision problem that inputs a 3-CNF sentence S, and outputs YES if S is satisfiable, and outputs NO if S is not satisfiable. Consider these four statements. A. 3-SAT is in P, but is almost surely not in NP B. 3-SAT is in NP, but is almost surely not in P C. 3-SAT is in P and is also in NP D. 3-SAT is neither in P nor in NP Determine which of these four statements is correct. Answer A, B, C, or D.
Transcribed Image Text:In Boolean logic, a sentence is in 3-Conjunctive Normal Form (abbreviated 3-CNF) if it of the form C1 ^ C2 ^ C3 ^ .…. A Cm, where S is the conjunction of m clauses, with each clause being a disjunction of S three literals. We say that S is satisfiable if there exists an assignment of TRUE/FALSE values to each variable so that the entire sentence S evaluates to TRUE. For example, in the last class, we showed that the following 3-CNF sentence, with m=8 clauses, is not satisfiable. D) ^ (B v č v D) ^ (c vĀ v D) ^ (A (A v (Bv č v D) A (c v Ā v D) a (A v B V C) ^ (a v B v C) A V v B v D) S = AVВV A V B Let 3-SAT be the decision problem that inputs a 3-CNF sentence S, and outputs YES if S is satisfiable, and outputs NO if S is not satisfiable. Consider these four statements. A. 3-SAT is in P, but is almost surely not in NP B. 3-SAT is in NP, but is almost surely not in P C. 3-SAT is in P and is also in NP D. 3-SAT is neither in P nor in NP Determine which of these four statements is correct. Answer A, B, C, or D.
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