![[UMN logo]](http://www.umn.edu/images/syssesqui.jpg)
CSci 4011: Formal Languages and Automata Theory
Fall 2008, University of Minnesota
Homework 1
Posted: Sept 2, 2008
Due: Sept 18, 2008
Reminder: Assignments are due in class before the start
of class on the day indicated.
Problem 1
Do part a of Exercise 1.4 from the book.
Problem 2
Do Exercise 1.12 from the book.
Problem 3
- Describe the language of Exercise 1.6 part L as the union of two
simpler languages.
- Describe DFAs that recognize the simpler languages.
- Use the construction of Theorem 1.45 to obtain an NFA recognizing
the language of Exercise 1.6 part L from the DFAs in the second part
of this problem.
Problem 4
- Use the construction that we described in class to obtain a DFA from
the NFA you have obtained in part three of Problem 3.
- Theorem 1.25 describes an alternative construction to obtain a DFA
for the language of Exercise 1.6 part L from the two DFAs you have
described in Problem 3 part 2. Carry out this construction.
- Contrast the two DFAs you have for the same language. If they are
the same, present a mapping between the states in the two that shows
they are the same. If they are different, the DFA that has more states
must have some states that are equivalent. Identify these states.
- Pick the DFA with the smallest number of states. Write a one
sentence description of what situation each state characterizes. For
an example of what is required here, consider the machine shown in
Figure 1.22 on page 44. The state q00 can be characterized here as one
in which at least the last two items in the input string seen so far
are 0s.
Problem 5
Do part a of Exercise 1.14 from the book. Note that when a problem
reads "Show that ...," what is needed is a proof.
Problem 6
Do Exercise 1.25 from the book.
Problem 7
Do Problem 1.31 from the book.
Problem 8
Do Problem 1.32 from the book.
Last updated on Aug 27, 2008 by gopalan atsign cs dot umn dot edu.