Chapter 7: Q25P (page 324)
Let is a satisfiable CNF-formula where each clause contains any number of literals, but at most one negated literal}. Show that .
Short Answer
This situation will be held true for .
/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none}
Learning Materials
Features
Discover
Chapter 7: Q25P (page 324)
Let is a satisfiable CNF-formula where each clause contains any number of literals, but at most one negated literal}. Show that .
This situation will be held true for .
All the tools & learning materials you need for study success - in one app.
Get started for free
Show that
Let ? be a 3cnf-formula. An ≠-assignment to the variables of ? is one where each clause contains two literals with unequal truth values. In other words, an ≠-assignment satisfies ? without assigning three true literals in any clause.
a. Show that the negation of any ≠-assignment to ? is also an ≠-assignment.
b. Let ≠SAT be the collection of 3cnf-formulas that have an ≠-assignment. Show that we obtain a polynomial time reduction from 3SAT to ≠SAT by replacing each clause ci
$$
with the two clauses
Where is a new variable for each clause, and b is a single additional new variable.
c. Conclude that -complete.
Modify the algorithm for context-free language recognition in the proof of Theorem 7.16 to give a polynomial time algorithm that produces a parse tree for a string, given the string and a CFG, if that grammar generates the string.
You are given a box and a collection of cards as indicated in the following figure. Because of the pegs in the box and the notches in the cards, each card will fit in the box in either of two ways. Each card contains two columns of holes, some of which may not be punched out. The puzzle is solved by placing all the cards in the box so as to completely cover the bottom of the box (i.e., every hole position is blocked by at least one card that has no hole there). It represents a card and this collection of cards has a solution}. Show that PUZZLE is NP-complete.
Let Analyse the algorithm given on page 185 to show that this language is in .
What do you think about this solution?
We value your feedback to improve our textbook solutions.