4003-389-01: Final Exam
Tuesday, November 16, 12:30-2:30pm, room 70-2590.
Topics
The emphasis of the final is on new stuff (described below)
and on overview questions.
You do need to know the main points of the material from weeks 1-5
(Sections 1.1-2.2), but not the details.
For example, you should know that NFAs are equivalent to FAs, but
you will not be required to apply the subset construction.
New stuff
You should have a good idea about the proofs from class but I will not ask you
to reconstruct them. You might be asked to prove similar statements to those on
the homeworks (e.g., apply the pumping lemma).
- Context-free languages: Section 2.3, and a brief overview of DCFLs (see slides)
- Turing machines: Sections 3.1-3
- Decidability/undecidability: Sections 4.1-2
- Proving undecidability via reductions: Sections 5.1-3
(except for linear bounded automata)
- Complexity: Sections 7.1-4
Notes
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The final will be closed book and notes,
but you may bring one sheet of letter-sized paper with your own
hand-written notes. You may write on both sides.
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Like the midterm, the final will consist of five questions
of equal weight.
Your lowest question score won't count. There might also be a bonus problem,
the same deal as with the midterm.
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The final 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 final.
Oversleeping, cars that don't start etc. do not constitute a valid excuse.
A note about the H1N1 flu sufferers without proper documentation: please let me know that you are sick *before* the exam.
The makeup exam might be in the form of an oral exam.
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To get some idea of the format of the final and the level of
difficulty of the questions, you can look at
(some sample problems).
Note: these problems were prepared by Professor Hemaspaandra for a 380/700 class that used a different book.
As such, here are some comments about the notation:
- Lambda is used instead of epsilon, the empty string.
- NFA-Lambda is an NFA that allows epsilon transitions.
- Recall that "recursively enumerable" means "Turing-recognizable" in the terminology
from our book. Also, "recursive" means "Turing-decidable".
- The term "Venn diagram" means the diagram that depicts subset relationships among
sets, like we were drawing for the Chomsky hierarchy.
This is just to get some idea. The sample questions do not guarantee
anything about the topics of the questions on your final and
it does not guarantee the exact level of difficulty
of the questions on your final.
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The final exam might also ask you to sketch the proof that a given problem is in NP.
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New: Here are answers to the practice problems.