4003-389-01: Midterm
The midterm will take place on October 11, 4-5:50pm, 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 and minimization of FA's
- Context-free grammars (CFG)
- Closure properties of regular and context-free 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, worth 5 points (thus you have a chance of getting up to 45 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 lose 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:
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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.
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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 epsilon
to denote the empty string; and also the NFA 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).
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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).
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To practice, I recommend to go through the Exercises and the Problems in the book.
Solutions to the sample midterm can be found here.
Note: I might have posted a 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.