CSCI 2670, Spring 2012

Introduction to Theory of Computing

Homework Assignment 3

Due Monday September 24, 2012 (Before the class starts)

(Unless otherwise specified, questions are selected from the textbook Michael Sipser, Introduction to the Theory of Computation, Second Edition, Thomson Course Technology.)

This homework assignment is about NFA, regular expressions, and the Pumping Lemma.

  1. Give two regular expressions for languages described in 1.6(d) and (e), respectively.

  2. Convert the following NFA to DFA.

  3. Give the regular expression for the language recognized by the DFA in the following Figure.

  4. Question 1.19(b) on page 86.

  5. Use the Pumping Lemma to prove that language
      L3 ={ ww-1 : w in {0, 1}* }
    is not regular, where w-1 is the reverse of string w.

  6. Questrion 1.30 on page 88.