4003-389-01: Final Exam
Tuesday, February 24, 12:30-2:30pm, room 70-2690.
Office Hours
There will be no regularly scheduled office hours during the finals week
but feel free to make an appointment or send e-mails with questions. I'll do
my best to answer them promptly.
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.
-
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.
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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
an old final (pdf).
Note: this is an old final from a 380 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.
- Ignore the part about unrestricted grammars (if you are interested, they are
equivalent to Turing machines, are similar to context free grammars but
on the left-hand side there can be more than just one variable, there could
be an entire string of variables and symbols of the alphabet).
- 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 old final does 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.
In fact, the old final is a little on the easy side.
The answers to the old final will be distributed in class.
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Some topics not touched upon by the practice final that have a good chance to appear in the
real final:
- Sketch the proof that a given problem is in NP.
- Apply a reduction (I promise, if it is on the final, it will not be complicated!),
similar level to what we did in Thm 5.4 (EQTM is undecidable).