91.304 Homework Assignments

2. Due Wednesday, February 6.
 The reversal of a string w, written as w^R, can be defined inductively
as follows:
      w^R =w = e        if w=e
    w^R= (ua)^R = au^R if w=ua, where a is a symbol and u a string.

^{Using mathematical induction, prove that, for any strings x and y,}
  (xy)^R = y^Rx^R

3. Due  Wednesday, February 13.
  Exercise 2.1, p. 54.
  Exercise 2.2, p. 54.
  Exercise 2.3, p. 55.
  Search the web for DFA simulators.  Find the best implementation
that closely approximates the conventions in TCGI, and illustrate
its execution on the DFA's of Exercises 2.1-2.3 (with appropriate
test strings as input).  In the homework that you turn in (hardcopies
only please), be sure to give the url where you find the best
simulator.

4. Due Thursday, February 21.
  Exercise 2.6, p.  55.
  Exercise 2.7, p.  55.
  Exercise 2.9, pp. 57-8.
Select a good DFA simulator from the web (see hw3), and illustrate
it's execution on the DFA's of Exercises 2.6 and 2.7.  Now
search the web for NFA simulators and select a good one that
closely approximates the conventions in TCGI.  Understand the
FA's of Exercises 2.6 and 2.7, as well as 2.9, to be NFA's.
Illustrate the execution of the NFA simulator that you selected
on the NFA's of Exercises 2.6, 2.7, and 2.9

5. Due Wednesday, March 6.
  Exercise 2.11, pp. 58-9.
  Exercise 2.12, p.  59.
In Exercise 2.11, parts (a)-(c), use a good NFA simulator to test the
input NFA's and a good DFA simulator to test the output DFA's.

6. Due Wednesday, March 13.
  Exercise 2.14(c), p. 60.
  Exercise 2.15(c), p. 60.
  Exercise 2.16(c), p. 60.
  Exercise 2.19(c), p. 61.
In Exercise 2.19(c), use a good NFA simulator to test the
the output NFA's.

7. Due Wednesday, March 27.
  Exercise 2.22(a), p. 62.
  Exercise 2.22(b), p. 62.
  Exercise 2.22(e), p. 63.

8. Due Wednesday, April 3.
  Exercise 2.25(b), p. 64.
  Exercise 2.26(a), p. 64.
  Exercise 2.34(a), p. 65.
  Exercise 2.35(a), p. 66.

9. Due Monday, April 22.
  Exercise 3.6,  p. 111.
  Exercise 3.10, p. 111.
  Exercise 3.14, p. 112.
  Exercise 3.22, p. 114.

10. Due Friday, May 3.
  Exercise 3.36,  p. 115.
  Exercise 3.37a, p. 116.
  Exercise 3.38a, p. 116.
  Exercise 3.39a, p. 116.