Midterm, 4003-389-01 Honors Introduction to CS Theory, Fall 2010

4003-389-01: Midterm

The midterm will take place on October 7, 4-5:20pm, in class. The midterm includes material covered in class in the first five weeks, namely (in more-or-less chronological order):

Languages and operations on languages and strings
(Deterministic) finite automata (DFA)
Nondeterministic finite automata (NFA)
Regular expressions
Pumping Lemma for regular languages
Myhill-Nerode Theorem
Closure properties of regular languages

Structure of the midterm. The midterm will consist of five problems for 10 points each. Your total score will be computed as the sum of the scores of the four highest scoring problems.

Bonus problem. There will also be a bonus problem, also worth 10 points (thus you have a chance of getting up to 50 points out of 40). Your solution must be essentially correct to receive points, in other words there is (almost) no partial credit for the bonus problem. The only case when you could receive a partial credit is if you have a correct idea but there is some minor technical problem, in which case you might loose a point or two.

Help-sheet. You may bring (and are encouraged to do so) one letter-sized double-sided "help-sheet" with your own hand-written notes (no printouts or photocopies). You are allowed to put anything you find fit on your help-sheet. Except for the help-sheet, the exam is closed notes and closed book. You do not have to memorize proofs from class or the book but you should understand them. You should be able to apply the constructions from the proofs, like the constructions for operations on languages (union, concatenation, etc. of two regular/context-free languages), NFA to DFA, regular expression to NFA, minimization of a DFA, etc.

Sample midterm can be found here. Some comments about the sample midterm:

I recommend to first solve the sample midterm and then look at the solutions posted below. Before you start solving, read through these comments regarding the notation and the selection of problems.
The sample midterm is a compilation of previously published sample exam questions and, in a couple of cases, does not follow our notation - namely lambda is used instead of little epsilon to denote the empty string; and also the NFA without epsilon transitions to DFA construction is called the subset construction. The sample midterm is intended to give you an idea about the type of problems you might see on the actual midterm, but please keep in mind that I cannot guarantee that the actual midterm will be of the same difficulty (mostly because difficulty is perceived very subjectively).
The sample midterm does not contain a bonus problem - if you want to practice those, try bonus problems from the book (I will not ask for a proof but I might ask for a construction that underlies a proof).
This is the sample midterm I published some time ago and at the time of the midterm, we had completely covered context-free grammars and pushdown automata. As such, the sample midterm contains 0.5+0.5 problems related to context-free languages whereas our midterm will not cover such problems. So, imagine a sample midterm with the "closure properties questions about context-free languages" being replaced by more closure properties questions about regular languages. Also, the "create a CFG" question could be replaced by a contruction question, e.g. apply the cartesian product construction to get the union of two regular languages, or possibly by a "create your own construction" question, such as the constructions from Theorems 1.45, 1.47, and 1.49.
The sample midterm's length reflects the usual time of 1 hour and 40 minutes. Our midterm will be scaled down somewhat to 1 hour and 20 minutes to accomodate the institute-wide honors dinner.
The sample midterm contain a problem that appears to need the minimization algorithm that we did not get a chance to cover by the end of week 4. However, this algorithm is not needed to solve the problem, knowledge from the first four weeks is perfectly sufficient.
For more sample problems involving the use of the pumping lemma to show nonregularity, see, e.g., Exercise 1.29 in the book (two of the three subproblems are solved - check the Selected Solutions section).

Solutions to the sample midterm can be found here. Note: I might have posted the wrong version of the solutions, though I tried not to. Please let me know if there are any problems/typos. The problem with the Myhill-Nerode theorem uses w instead of z.

The midterm can not be made up except for real emergencies in which case proper documentation (like a doctor's note) will be required. If at all possible, you should contact me prior to the midterm. Oversleeping, cars that don't start etc. do not constitute a valid excuse.