CSC 456/656 Assignment 6

Due date, November 20, 2003, 4:00 PM.

• Help me prepare a study guide for the final exam, by contributing to my list of decidable and undecidable problems. (Hint: look at pages 169 and 170 of your textbook.) This problem is an exception to the rule of not handing in electronic copy. I want a handwritten version (for grading purposes) but I also want an electronic copy so that I can add it to the file. The electronic version will not be graded.
• Work the following problem but do not turn it in.
  Let N be the set of all natural numbers. Every infinite subset S of N can be enumerated by the following simple algorithm, which I learned as a freshman mathematics student.
  1. Write down the smallest element of S, say n.
  2. Delete n from S.
  3. Go to step 1.
  Your problem is to show what is wrong with the above algorithm. (For some reason, when I was a freshman, none of the math professors thought there was anything wrong with it. But you can see, can't you?)
• Work, but do not hand in these questions:
  1. True of False: It is not known whether every NP-complete problem is undecidable.
  2. What is a public-key encryption system? What does that have to do with the question of whether P = NP? (Go to the internet and get some articles.)
  3. What is RSA (Rivest-Shamir-Adelman) coding used for in practice nowadays? (Go to the internet and get some articles.)
  4. Compare RSA coding to the most sophisticated encryption methods used during World War II. (Go to the internet and get some articles.)
  5. How did a United States Government agency try to limit RSA coding? How did this effort fail? (Go to the internet and get some articles.)
  6. Edgar Allen Poe's character, in the short story, ``The Gold Bug," said that any encryption system devised by man can be broken by man. What is your opinion on this? (Go to the internet and get some articles.)