CSCI 2670, Spring 2012

Introduction to Theory of Computing

Homework Assignment 7

Due Monday Nov 26, 2012

(Unless otherwise specified, questions are selected from the textbook Michael Sipser, Introduction to the Theory of Computation, Second Edition, Thomson Course Technology.)
  1. Question 3.2 (d) and (e), page 159.

  2. Question 3.8 (b), page 160. Note that an implementation-level description is one that formally defines a transition function or a state diagram for the desired Turing machine.

  3. Question 3.9 (a), page 160. Hint: you may just need to show a known language (e.g, {anbncn : n ≥ 0}) that is not recognizable by any 1-PDA but can be recognized by a 2-PDA.

  4. Question 3.9 (b), page 160. Additional hint: Using the first stack to store the tape content of the simulated TM. The current head position corresponds to the top of the stack. When the head moves to the right, a content is pushed to the stack. The tricky part is when the head moves to the left, the first stack needs to pop. The issue is how to use the second stack to store the contents popped from the first stack.

  5. Question 3.15 (d), page 161. And show how the proof may not be applicable to Turing recognizable languages.