CS 314 Day 1: January 22, 2008 Item #1. Proofs formal and informal, Mathematics. Theorem: A set of n elements has 2n subsets. Proof (Exercise 1, p. 13): First, an informal proof. Let each subset be represented by a binary number with n digits. For ex
Questions for EZQuiz 4
Formal contrapositive of pumping lemma with all 4 quantiers, from pumping lemma handout.
Rephrasing the formal contrapositive as a game, from pumping lemma handout. You can
omit the parts in parentheses.
Linz examples 4.9, 4.12,
COMP 314 Homework Assignment 8
1. Explain why each of the following problems is in PolyCheck. Be sure to indicate
which, if any, of the caveats in the denition of PolyCheck are used.
(a) (5 points) The threshold version of the traveling salesperson proble
COMP 314 Homework Assignment 7
1. (5 points) Examine the program sillySort.py, distributed with the code for class 17.
What is the nondeterministic running time of this program? (Dont be too concerned
with details in your answer. At a minimum, state wheth
COMP 314 Homework Assignment 5
1. (14 points) For each of the problems given below, circle each complexity class the
problem is known to be a member of.
COMP 314 Homework Assignment 6
1. (20 points) Download the dfa code provided for this assignment as dfa.zip. Read the
JavaDoc rst. Then read the code itself. Finally, complete the code of the accepts()
method in the Dfa class. Submit a hard copy of your c
COMP 314 Homework Assignment 3
1. (a) (10 points) Using a reduction from a problem that has already been proved
undecidable in this class, prove that the following problem is undecidable. Given a
Turing machine T , and input I , and a particular state s i
COMP 314 Homework Assignment 2
Note: For the rst two questions, it is probably easiest to use JFLAP to implement and
test your machine. You can submit a printout from JFLAP as your machine description.
However, hand-drawn solutions are also permissible. Y
COMP 314 Homework Assignment 3
1. (8 points) For each of the four statements below, indicate whether the statement is
provable and/or true in each of the logical systems dened in the reading, by placing
checkmarks in the tables below.
Dickinson College CS 314 / MA 314 Theoretical Foundations of Computer Science Syllabus, Spring 2008 Catalogue Description "314 Theoretical Foundations of Computer Science An introduction to the theory of computation. Topics include formal language th
CS314 homework 3 solutions, January 31, 2008 Here are some suggested solutions to 1.3(3, 14). 3. Here's a possible grammar, G = <N,T,<double>, P>. Of course, N and T are implied by the set of productions without your having to state them explicitly.
CS 314 Day 4: January 31, 2008 Item #9. Errata for Day01.pdf, typographical errors only. In Item #1, It Item #2, there this many there are this many #4 #6
Item #10. Second Three Homework Text Exercises. 2.1 For the problems that I starred (*) below,
CS 314 Day 7: February 12, 2008, Version 2.0a Item #11. More errata found. On my class handouts: In Item #9 , It In In Item #10, 10* 10a* [as mentioned on the list server] On Postmortem 4, page 2, bet met In the textbook, but not in the author's t
CS 314 Day 11: February 26, 2008, Version 1.0 Item #15. Homework assignments up to Spring Recess. Assigned Day 10 for Day 11: Read 4.1, 2 and do 4.1(2a, 5, 6, 17) What does it mean to have a problem assigned whose answer is in the back of the book? A
CS314 Day 14: March 6, 2008, Version 3.0 Item #18. Homework assignments for week after Spring Recess. Day 15, March 18: Section 5.1, Exercises 2, 3, 5, 7b, 8c, and 22. [7b was not assigned in earlier versions] I did not lecture on this very easy mate
Day 15, March 18, 2008, Version 2.0 Item #20. Brief comments on 5.1,2. These sections are really too easy for you to need my lecturing on them, but I'll provide a few background comments. In 5.1 we see that a regular grammar is a special case of a co
Day 17, March 25, 2008. Version 1.0 Item #22. Homework assignments for today and Thursday, March 27, 2008. This repeats what was on the whiteboard on Day 16. Day 17, March 25. Read 5.2, 5.3. Do 5.2 (1, 4, 7, 8, 13). Day 18, March 27. Read 6.1, 6.2. D
Day 19, April 1, 2008. Version 2.0
Item #26. Homework assignments through April 10. Thursday, April 3: Individual assignment: 7.2 (15). Grade will be combined with your second team assignment that you turned in today. Tuesday, April 8, or Thursday,
Day 22, April 10, 2008, Version 1.0 Item #27. Homework assignment due Day 23. Due on Day 23, Tuesday, April 15: I see that I assigned homework for 6.1, 2 and 7.1, 2 but didn't say in writing to read those sections. Read them! But the proofs won't be
Day 23, April 15, 2008, Version 1.0 Item #28. Homework assignments giving practice with turing machines. Due on Day 24, Thursday, April 17: Read the rest of 9.1. Individual written assignment: Work problems 9.1(3, 4, 5, 6, 9). Due on Day 25, Tuesday,
Day 24, April 17, 2008, v1.0 Item #30. A sample homework solution for a turing machine (tm) problem. I was going to do this one on the whiteboard today, but in our discussion of other issues I didn't get this far. It's just as well, since carefully d
A solution to 1.2(3) by Dr. Gene Chase. January 31, 2008. Version 1.0 To prove: for all strings w , G*, (wR)R = w. Let's prove it by induction on the length n of the string w. (1)
First, I see that the definition of reverse is given informally on p.
COMP 314 Homework Assignment 1
1. (5 points) Use proof by contradiction to prove that any string of 30 lowercase letters contains
at least one letter twice.
2. (2 points) Fill in the nal column of the following table, assuming all programs are as dened