Directions: Question 1 consists of five statements to be marked "true", "false", or "unknown", with no justification needed. Here "unknown" means "not resolvable by the results in this course". No justification is needed or wanted, and there is no penalty for a wrong guess.
Questions 2 and 3 each consist of a true statement that you are to prove. As these statements were proved in lecture, you may not simply quote their proofs -- give an explanation in your own words of why they are true that demonstrates your understanding.
Questions 4 through 8 are similar to those on the midterm. There is a statement which is either true or false. You will get five points for a correct boolean answer, and there is no penalty for guessing. Then JUSTIFY YOUR ANSWER -- the five remaining points will be awarded based on the degree to which your answer is correct and convincing.
Altogether there are eight questions for 100 points.
Crib sheet: I will state some useful definitions after the questions.
(off-campus) Due to my error, off-campus students got a question repeated from the practice exam:
Every context-free language is recursively enumerable (r.e.).
If M is any one-tape Turing machine, the language VALCOMPM is in L. Here VALCOMPM is the set of strings that denote accepting computations of M on some input.
If a language A is in NP, then A ≤ QSAT, where "≤" denotes L-reducibility.
Every language in L is context-free.
Unless P = NP, there is no poly-time algorithm that approximates that optimal solution to BIN-PACKING within a factor of three (i.e., uses at most three times the optimal number of bins).
Last modified 3 June 2003