CS 162 - Automata Theory Homework 7, 50 Points
Due: Friday, March 16, 11:55pm

  1. 10 points. Exercise 7.21 from Sipser.
  2. 10 points. Problem 7.22 from Sipser.
  3. 10 points. In the SET-COVER problem, we are given a set of elements, {1, 2, ..., m}, called the universe, and a set S of n sets whose union equals the universe. We are also given an integer, k, and asked if there is a collection of k sets in S such that the union of the sets in this collection equals the universe. Show that SET-COVER is NP-complete.
  4. 10 points. Problem 7.35 from Sipser.
  5. 10 points. Problem 7.54 from Sipser.