This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CS 154 Intro. to Automata and Complexity Theory Handout 25 Autumn 2006 David Dill November 14, 2006 Problem Set 6 Due: November 28, 2006 Homework: (Total 100 points) Do the following exercises. Problem 1. [20 points] Prove that the following problem, called 4TASAT, is NPcomplete. The problem is defined as follows: INPUT: A boolean formula F ( X 1 , X 2 , . . . , X n ). PROBLEM: Does F have at least 4 satisfying truth assignments? You should reduce the 3SAT problem to 4TASAT. The answers to the following questions constitute the proof of NPcompleteness. (a). Prove that 4TASAT is in NP. (b). Describe a polynomialtime reduction from 3SAT to 4TASAT. Your reduction should take a 3SAT formula F and construct an instance of the 4TASAT problem, say the formula G . ( Hint : Suppose you add a variable Y to the boolean formula F , but dont actually use it in any of the clauses. If F had k satisfying truth assignments originally, how many satisfying truth assignments will it have now?) (c). Show that F is satisfiable if and only if G has at least four satisfying truth assignments. Problem 2. [20 points] Prove that the following problem called DS (Dominating Set) is NP complete. A dominating set in a graph G = ( V, E ) is a set of vertices S...
View
Full
Document
 Winter '08
 Motwani,R

Click to edit the document details