CSCI 2670, Fall 2012

Introduction to Theory of Computing

Homework Assignment 8

Due Dec 4, 2012 (5:00pm)

(Unless otherwise specified, questions are selected from the textbook Michael Sipser, Introduction to the Theory of Computation, Second Edition, Thomson Course Technology.)
  1. Question 4.1 (exercise only, you do not need to turn in your answers; solutions are given on page 185).
  2. Question 4.2 page 183.

  3. Question 4.3 page 183

  4. Question 4.4 page 183.

  5. Read and understand the proof of Theorem 4.11 (the proof is on pages 179-181). Use succinct logical reasoning statements to rewrite the proof. You can only use succinct logical statements, assumptions, and/or inferences, with a total up to 20 sentences. Each sentence can be at most one line long. Number these sentences and they are connected logically in a sequence.

  6. Question 5.1 page 211. (Hint: reduce language ALLCFG to language EQCFG. ALLCFG is proved to be undecidable in Theorem 5.13).

  7. Question 5.4 page 211.

  8. Questions 5.6 and 5.7 (exercise only, you do not need to turn in your answers; solutions are given on page 214)