CS 3512 Final Exam Topics
Topics covered on Exam #1
Topic Text Chapter
-------------------- -------------
Elementary Notions and Notations.. 1
A Proof Primer.................. 1.1
Sets............................ 1.2
skip 1.2.4
Ordered Structures.............. 1.3
Graphs and Trees (skip)......... 1.4
Facts About Functions............. 2
Definitions and Examples........ 2.1
2.1.1 only - skip the rest
(but useful elsewhere in CS)
Constructing Functions.......... 2.2
skip 2.2.2 (Map function) for now
Properties of Functions......... 2.3
skip 2.3.4 and 2.3.5
Countability.................... 2.4
Topics covered on Exam #2
Topic Text Chapter
-------------------- -------------
Construction Techniques........... 3
Inductively Defined Sets........ 3.1
skip 3.1.5
Recursive Functions & Procedures 3.2
skip 3.2.6
Grammars - skip for now ........ 3.3
Inductive Proof................... 4
skip 4.1, 4.2, 4.3
Inductive Proof................. 4.4
skip Example 4.47 for now
Analysis Techniques............... 5
skip 5.1 through 5.5
Comparing Rates of Growth....... 5.6
skip "Divide & Conquer Recurrences
(pages 381-389)
Topics covered since Exam #2
Topic Text Chapter
-------------------- -------------
Regular Languages & Finite Automata 11
Regular Languages................ 11.1
Review Properties of R.E.s p. 700
Finite Automata.................. 11.2
skip examples 11.5, 11.6, & 11.7
skip 11.2.3 (done better in 11.3.1)
For 11.2.4, know the formula on
page 713 for new(i,j) (in "Eliminate
State k")
skip 11.2.5
skip 11.2.6 but understand T and T*
as in the lecture notes
Constructing Efficient Finite
Automata ..... 11.3
11.3.1 Know how to do the regular
expression to NFA-Lambda algorithm
11.3.2 Know that the crucial step
in going from an NFA to a DFA is
that the states of the DFA are
sets of states of the NFA - this
is the "Subset Construction" of
the Chapter 11 notes.
Regular Languages Topics -Skip-.. 11.4
Also, from the Chapter 11 notes, know:
1) Regular languages are closed
under union, concatenation, and
star (by definition), and also
complement, intersection, and
set difference.
2) DFA's, NFA's, and NFA-Lambdas
are all equivalent: language
L is recognized by a DFA iff
L is recognized by an NFA iff
L is recognized by an NFA-Lambda
(see 11.3.2 above)
Distinguishability (only in the notes)
Know how stings are distinguished by
a language L.
Know the "Distinguishability Theorem"
If there are n strings that are
distinguishable from one another,
any DFA recognizing L has >= n states
Know the "Distinguishability Corollary"
If there is an infinite set of strings,
each distinguished from the others by
L, then L is not regular.
Know the "Minimal DFA Theorem": the
indistinguishability classes are the
states - this is minimal by the
Distinguishability Theorem
Know what Kleene's Theorem says: a
language is regular (represented by
a regular expression) iff it is
recognized by a DFA.
Grammars, PDA's, Turing Machines
Grammars ....................... 3.3
skip 3.3.1 (English grammar)
Know 3.3.2, 3.3.3, 3.3.4 up to
"Decimal Numerals, 3.3.5
Know the definition of a grammar
Know that a grammar generates a
language
Know that grammars can be combined
by the union, concatenation, &
star constructions
Know that some grammars are
ambiguous
Context-Free Languages/PDA's .... 12
Context-Free Languages ........ 12.1
Know the definition
Know CFL's are closed under union,
concatenation, and star
Pushdown Automata ............. 12.2
Know they are non-deterministic
Know Theorem 12.6 ......... 12.2.2
CFL's = langs. accepted by PDA's
Turing Machines ................. 13
Turing Machine Definition ... 13.1
Church-Turing Thesis ........ 13.2
Know what this says (page 829)
Computation ..................... 14
Computability ............... 14.1
Know that some problems have no
algorithmic solution - e.g. the
Halting Problem
The Hierarchy of Languages .. 14.2
Know the contents of the table
on the last page of the notes
Exercises for Exam #1
The following is a list of Exercises from the
text like the ones that may appear on exams,
possibly in a slightly altered forms. Some
have been assigned as homework. Also, you
should know how to do (or at least understand)
the "Additional Problems" from "Recommended
Problems" 1 through 6.
Chapter 1
1.1 Exercises (pages 12-13):
All exercises, especially 2 c, d, and e,
3 b, and d, 4 c, 5, and 7 d, which were
assigned as homework.
1.2 Exercises (pages 32-36):
All exercises except 24-26 (not covered),
but especially 3 b, d, f, and h, 5,
6 a, 7 a, 8, and 19, which were assigned
as homework. Also, 13, 14, and 35 are of
low priority.
1.3 Exercises (pages 53-56):
All exercises except 19-21,
but especially 2 f, 4 d, 8 b and e,
10 b and d, 11 b, 12 b, and 14 a,
which were assigned as homework
1.4 - Skip this section.
Chapter 2
2.1 Exercises (pages 92-96):
Exercises 1, 2, 9, 15, 16, 27, and 28,
but especially 2, 5 b and c, 27 b and c,
and 28 c, d, and e, which were
assigned as homework.
2.2 Exercises (pages 104-106):
Skip all of these for now.
2.3 Exercises (pages 117-121):
Exercises 1-3, 4 a, b, e, 5 c, f, g,
15-18. None of these were assigned
as homework, but related questions
appeared as "Additional Problems" in
"Recommended Problems 5".
2.4 Exercises (pages 130-131):
All exercises, but especially 1 a, 2 f,
3 a and d, and 9. Also, ""Additional
Problems" 3 and 4 of "Recommended
Problems 6" were assigned as homework.
Exercises for Exam #2
The following is a list of Exercises from the
text like the ones that may appear on exams,
possibly in a slightly altered forms. Some
have been assigned as homework. Also, you
should know how to do (or at least understand)
the "Additional Problems" from "Recommended
Problems" 7 through 9 (it might be useful
to review "Recommended Problems" 10 also
in order to understand asymptotic notation
better).
Chapter 3
3.1 Exercises (pages 148-151):
All exercises except 5, 11, 16 - 18, 20,
and 21.
3.2 Exercises (pages 173-178):
All exercises except 7, 13, and 20 - 26.
Chapter 4 - just Section 4.4
4.4 Exercises (pages 274-278):
All exercises except 18, and 22 - 25.
Chapter 5 - just Section 5.6
5.6 Exercises (pages 389-392):
All exercises except 10 - 13.
Exercises since Exam #2
The following is a list of Exercises from the
text like the ones that may appear on exams,
possibly in a slightly altered forms. Some
have been assigned as homework. Also, you
should know how to do (or at least understand)
the "Additional Problems" from "Recommended
Problems" 10 through 12 (though 10 was partly
covered on Exam #2, it might be useful to
review "Recommended Problems" 10 also in
order to understand asymptotic notation
better).
Chapter 11
11.1 Exercises (pages 702-704)
Exercises 1-4, 8, 9
11.2 Exercises (pages 726-728)
Exercises 1-6
11.3 Exercises (pages 743-745)
Exercises 1, 3b, 12
Distinguishability
There are no exercises on this from
the text, but "Recommended Problems" 12
has some.
Grammars, PDA's, Turing Machines
You don't have to know how to do any
exercises from the sections that cover
this "Survey" material, but you should
know the definitons and results mentioned
above, including the Church-Turing Thesis