4003-380-01: Homework, Reading and Slides
Week 1
- Slides for this week: Introduction (Chapter 0) - pdf (ppt),
Finite Automata (Section 1.1) - pdf (ppt)
-
Tuesday, Sept 7
- Covered in class: Course logistics.
- Covered in class: Chapter 0, introduction to CS theory, strings, and languages.
- Next class: Discrete math quiz, September 9, 2:00-2:30pm. There will be two problems. First, a basic discrete math reading,
writing, reasoning question. Second, a proof by mathematical induction (the simplest form of mathematical induction going from i to i+1,
see Section 0.4, pages 22-25, for an interesting example from real life). Feel free to download a
sample quiz. I recommend to use our
tutoring center for help.
- A note for students with disabilities:
RIT is committed to providing reasonable accommodations to students with disabilities.
If you would like to request accommodations such as special seating, testing modifications,
or note taking services due to a disability, please contact the Disability Services Office.
It is located in the Eastman Building, Room 2342; the Web site is www.rit.edu/dso.
After you receive accommodation approval, it is imperative that you see me during office hours
so that we can work out whatever arrangement is necessary.
Thursday, Sept 9
- In class: Discrete math quiz (30 min).
- Covered in class: solutions of the DM quiz.
- Covered in class: finished strings and languages (Chapter 0), started finite automata (Section 1.1)
Homework 1, due Friday, Sept 17, 2010, 4pm: pdf
Remark: The homework asks you to design several finite automata. So far we covered only the motivational automatic door example.
Read ahead through the first part of Section 1.1 to solve the automata problems over the weekend. Or, solve the other problem first and wait
until Tuesday with the finite automata - we will see several examples of finite automata on Tuesday in class.
Week 2
- Slides for this week: in addition to last week's slides, Nondeterministic finite automata (Section 1.2) - pdf (ppt)
-
Tuesday, Sep 14
- Covered in class: Section 1.1 (definition of finite automata, examples, introduction to closure properties of regular languages)
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Thursday, Sep 15
- Covered in class: finished Section 1.1 (closure properties of regular languages: union, intersection, difference, complement, concatenation)
- Covered in class: introduction to nondeterministic finite automata (Section 1.2)
- Homework 2, due Friday, Sept 24, 2010, 4pm: pdf
Week 3
- Slides for this week: Regular Expressions (Section 1.3) - pdf
(ppt)
-
Tuesday, Sep 21
- Covered in class: formal definition of NFAs and their computation, converting NFAs to DFAs (the subset construction,
and getting rid of the epsilon transitions) - Section 1.2.
-
Thursday, Sep 23
- Covered in class: finished Section 1.2, started Section 1.3 (think about the regular expression examples on the last slide from class)
- I hoped to cover the solution of Homework 1 Problem 5 in class but we ran out of time. Here is a sketch (if you are having troubles understanding what is happening, visit the tutoring center):
L5 has 5 states, with a-arrows forming a directed loop through all five states and b-arrows forming self-loops; the start state is also the only accept state.
Formally, M=(Q,{a,b},delta,q0,{q0}) where Q={q0,q1,q2,q3,q4} and delta(qi,b)=qi and delta(qi,a)=q(i+1)mod 5
for every i in {0,1,2,3,4}. For any k>0, we define:
Mk=(Q,{a,b},delta,q0,{q0}) where Q={q0,q1,...,qk}
and delta(qi,b)=qi and delta(qi,a)=q(i+1)mod k
for every i in {0,1,2,..,k}.
This solution should look familiar, as we were doing something similar (though, of course, different languages) in class about a week ago.
- Other solutions of Homework 1: Problem 1,
for other problems, please visit the tutoring center.
- Note about grades for Homework 1 on MyCourses: due to a misunderstanding between me and our grader, the total number of points was set to 22,
not 26. Thus, our grader recomputed the grades as out of 22 and entered them to mycourses. This means that the percentage you
see is correct but the actual points seem weird. E.g., if you scored 21 points out of 26, or about 80.77%, the grade will show 80.77%
and it will also show 17.769 out of 22 (which is also 80.77%).
We certainly hope to have the maximum number of points set up properly for all future homeworks.
- Homework 3, due Friday, October 1, 2010, 4pm: pdf
Week 4
- Slides for this week: Myhill-Nerode Theorem and Minimization of DFAs - pdf
(ppt)
-
Tuesday, Sep 28
- Covered in class: regular expressions (Section 1.3)
- Homework 2 solutions are here and
here.
-
Thursday, Sep 30
- Covered in class: finished the NFA -> regular expression construction.
- Covered in class: the Myhill-Nerode Theorem and minimization of finite automata
- Homework 4, due Friday, October 8, 24, 2010, 4pm: pdf
Week 5
- Slides for this week: Nonregular Languages (Section 1.4) - pdf
(ppt),
Context-free grammars (Section 2.1) - pdf
(ppt)
-
Tuesday, Oct 5
- Covered in class: finished the minimization algorithm for DFAs
- Covered in class: pumping lemma and its use in proving nonregularity
- Covered in class: solution of problem 2 and proving nonregularity by closure properties
- Solutions of homework 3 problems can be found here
and here and
here.
-
Thursday, Oct 7
- Covered in class: finished examples of proofs of nonregularity using the pumping lemma
- Covered in class: started context-free grammars (Section 2.1)
- Covered in class: review of closure properties and other midterm material
- Recall that the midterm takes place next week,
Thursday, 2-3:50pm, in class. More info about the midterm can be found on the midterm website.
- No homework due Friday, 10/15/10. Homework 4 answers can be found here
and here.
Week 6
- Slides for this week: Pushdown automata (Section 2.2) - pdf
(ppt)
-
Tuesday, Oct 12
- Covered in class: finished CFGs, including closure properties and ambiguity
-
Thursday, Oct 14
- Homework 5, due Friday, October 22, 2010, 4pm: html
Week 7
- Slides for this week: Non-context-free languages (Section 2.3) - pdf
(ppt)
-
Tuesday, Oct 19
- Covered in class: solutions of the midterm exam
- Covered in class: finished ambuguity, Chomsky normal form, started pushdown automata
-
Thursday, Oct 21
- Covered in class: revisited Chomsky normal form, finished pushdown automata (including the CFG -> PDA construction),
pumping lemma for context-free languages (Section 2.3)
- Homework 6, due Friday, October 27, 2010, 4pm: pdf
Week 8
- Slides for this week: Turing Machines (Section 3.1) - pdf
(ppt),
Variants of Turing Machines (Section 3.2) - pdf
(ppt),
Defining Algorithm (Section 3.3) - pdf
(ppt),
Decidable Languages (Section 4.1) - pdf
(ppt)
-
Tuesday, Oct 26
- Covered in class: Turing machines (Section 3.1)
- Homework 5 solutions can be found here.
Please note that alternative correct solutions exists for several of the homework problems.
-
Thursday, Oct 28
- Covered in class: variants of Turing machines (Section 3.2), Church-Turing thesis (Section 3.3), started decidability (Section 4.1)
- Homework 7, due Friday, November 5, 2010, 4pm: pdf
Week 9
- Slides for this week: Undecidable problems (Section 5.1) - pdf
(ppt)
-
Tuesday, Nov 2
- Covered in class: Decidable languages (Section 4.1), our first undecidable problem: the acceptance problem (Section 4.2), our first reduction: showing that the acceptance problem reduces to the halting problem, thus, the halting problem has to be undecidable as well (Section 5.1)
- Solutions of Hw6 can be found here. Please note that the solutions use nonstandard notation: the transitions use semi-colons instead of arrows, lambda is being used instead of epsilon, etc.
-
Thursday, Nov 4
- Class canceled due to sickness. We will have a make-up class (the final review) scheduled on Thursday of the final exam week.
- Homework 8, due Friday, November 12, 2010, 4pm in the tutoring center or by Sunday, November 14, 8pm on MyCourses (you may also hand in your solutions directly to me in person; no other submission options are allowed):
html
Week 10
