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CSci 4011: Formal Languages and Automata Theory
Fall 2008, University of Minnesota
Homework 4
Posted: Oct 16, 2008
Due: Before class on Oct 30, 2008
Problem 1
Provide a formal description for the Turing machine described in
Example 3.11. By formal description is meant a description like that in
Example 3.9 on page 145.
Problem 2
Do Exercise 3.8 parts b from the book.
Problem 3
Do Exercise 3.6 from the book.
Problem 4
Do Exercise 3.7 from the book.
Problem 5
Read Problem 3.9 to understand what a k-PDA is. There may be a little bit
of an ambiguity in the description in that it is not clear if the
transition to the next state depends on the top of stack symbol on all
stacks or just one stack. Assume the former. Now do the following:
- Show that a k-PDA can be simulated by a Turing machine for any
k. You may find it convenient to use multitape Turing machines and
Theorem 3.13 for this part.
- Show that a Turing machine can be simulated by a 2-PDA.
Hint: We can think of capturing what is on the tape of the
Turing machine between the stack of a 1-PDA and the input
tape. However, we have difficulty in
realizing a left movement of the head with such a machine. But perhaps
the second stack will be helpful for this? If you follow this line of
thinking, you should describe a translation from the Turing machine
transition function to one for a 2-PDA from which it should be clear
that the two accept the same language.
Problem 6
Do Problem 3.11 from the book.
Problem 7
Do Problem 3.13 from the book.
Problem 8
Do Problem 3.16 all but part a from the book.
If you compare this with Problem 3.15, you see that complementation
has been left out. Think about whether or not this is necessary. You
do not need to turn in anything for this part, but thinking about this
now should help with regard to the next chapter.
Last updated on Oct 16, 2008 by gopalan atsign cs dot umn dot edu.