Consider the reduction from 3-CNF-SAT to SUBSET-SUM. For the formula ϕ = (x1 ˅ ¬x3 ˅ x4) ˄ (¬x1 ˅ x3 ˅ x4) ˄ (¬x1 ˅ x2 ˅ ¬x4), construct the following values in the set S: v1, v1’, v2, v2’, v3, v3’, v4, v4’. Note that the formula has four variables: x1, x2, x3, and x4. It has three clauses: C1 = (x1 ˅ ¬x3 ˅ x4), C2 = (¬x1 ˅ x3 ˅ x4), and C3 = (¬x1 ˅ x2 ˅ ¬x4).
Consider the reduction from 3-CNF-SAT to SUBSET-SUM. For the formula ϕ = (x1 ˅ ¬x3 ˅ x4) ˄ (¬x1 ˅ x3 ˅ x4) ˄ (¬x1 ˅ x2 ˅ ¬x4), construct the following values in the set S: v1, v1’, v2, v2’, v3, v3’, v4, v4’. Note that the formula has four variables: x1, x2, x3, and x4. It has three clauses: C1 = (x1 ˅ ¬x3 ˅ x4), C2 = (¬x1 ˅ x3 ˅ x4), and C3 = (¬x1 ˅ x2 ˅ ¬x4).
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 14E: Assume that is a binary operation on a non empty set A, and suppose that is both commutative and...
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Consider the reduction from 3-CNF-SAT to SUBSET-SUM. For the formula ϕ = (x1 ˅ ¬x3 ˅ x4) ˄ (¬x1 ˅ x3 ˅ x4) ˄ (¬x1 ˅ x2 ˅ ¬x4), construct the following values in the set S: v1, v1’, v2, v2’, v3, v3’, v4, v4’. Note that the formula has four variables: x1, x2, x3, and x4. It has three clauses: C1 = (x1 ˅ ¬x3 ˅ x4), C2 = (¬x1 ˅ x3 ˅ x4), and C3 = (¬x1 ˅ x2 ˅ ¬x4).
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