4003-389-01: Homeworks, Reading and Slides

Week 1

• Slides for this week: Introduction - pdf (ppt), Finite Automata - pdf (ppt), Nondeterministic Finite Automata - pdf (ppt)


• Tuesday, Sept 4
  • Covered in class: Course logistics.
  • Covered in class: Strings & Languages (Chapter 0), started (Deterministic) Finite Automata (Section 1.1)
  • Note: Due to the GCCIS Honors Dinner on Thursday, September 6, we will finish class at 5pm. There will be assigned reading to make up for the lost class time.
  • 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 6
  • Covered in class: (Deterministic) Finite Automata (Section 1.1)
  • Took a field trip to the GCCIS Honors Dinner.
  • Read the "Regular operations" part of Section 1.1, including Theorem 1.25 (pages 44-46). The Theorem states that if A1 and A2 are languages recognized by finite automata M1 and M2 (i.e. A1 and A2 are regular), then there is a finite automaton M for the union of A1 and A2.
    What happens when you apply the proof to the languages L1 and L2 we discussed in class today? How many states does the resulting automaton have?


• Homework 1, due Thursday, 09/13, 4:00pm: click here

• Slides for this week: Nondeterminism - see Week 1, and Regular Expressions - pdf (ppt)


• Tuesday, Sept 11
  • I am posting a sample Discrete Math quiz to give you an idea about the type of problems we ask students in 4003-380.
  • Covered in class: closure properties of regular languages (finished Section 1.1), started NFAs (Section 1.2)
  • Hw1 due next class.


• Thursday, Sept 13
  • Covered in class: formal definition of NFAs, equivalence of NFAs and DFAs (Section 1.2)
  • Covered in class: solutions of Hw1, Problem 1


• Homework 2, due Thursday, 09/20, 4:00pm: click here

Bonus problems - no due date: Exercise 1.45, page 90, and Exercise 1.57, page 92. It suffices to give the constructions, you do not have to prove their correctness. (I might ask you for the proof if I am having troubles verifying your construction - but hopefully that will not happen. :)
Please hand in your bonus problems on separate sheets of paper, not with your other homework problems.
(Note: as with most other courses, there is no partial credit for bonus problems.)

• Slides for this week: Regular expressions - see week 2, and Nonregular Lanuages - pdf (ppt)


• Tuesday, Sept 18
  • Covered in class: closure properties using NFAs, started regular expressions (Section 1.3)
  • Hw2 due next class.


• Thursday, Sept 20
  • Covered in class: finished the proof of Kleene's Theorem (Section 1.3), started non-regular languages (Section 1.4)


• Homework 3, due Thursday, 09/27, 4:00pm: click here

• Slides for this week: Nonregular Languages - see Week 3, Myhill-Nerode Theorem - pdf (ppt)


• Tuesday, Sept 25
  • Covered in class: Pumping Lemma (Section 1.4)
  • Hw3 due next class.


• Thursday, Sept 27
  • Covered in class: the Myhill-Nerode Theorem and minimization of finite automata (see Problems at the end of Chapter 1 and Problem 7.42 on page 327)


• Homework 4, due Thursday, 10/04, 4:00pm: click here

• Slides for this week: Context-free Grammars - pdf (ppt), Pushdown Automata - pdf (ppt)


• Tuesday, Oct 2
  • Covered in class: context-free grammars (Section 2.1), closure properties of CFLs
  • Hw4 due next class.


• Thursday, Oct 4
  • Covered in class: closure properties continued, ambiguity, Chomsky normal form
  • Covered in class: solutions of Problem 5 on Hw4
  • No homework due next week due to the midterm on Thursday, October 11, 4-5:50pm. Follow the posted link for more information about the midterm.

• Slides for this week: see the slides posted last week


• Tuesday, Oct 11
  • Covered in class: solutions of Hw3, Hw4, midterm review
  • Covered in class: pushdown automata (Section 2.2)
  • Reminder: midterm next class.


• Thursday, Oct 13
  • In class: midterm.


• Homework 5, due Thursday, 10/18, 4:00pm: click here
  Bonus problems, no due date: Problem 2.22, page 156, and Problem 2.42, page 158 (the same problem numbers but pages 130 and 131 in the second edition).

• Slides for this week: Non-context-free languages - pdf (ppt), Turing Machines - pdf (ppt)


• Tuesday, Oct 16
  • Covered in class: formal PDA definition, equivalence of PDAs and CFGs (CFG to PDA)
  • Covered in class: midterm problem solutions, including the bonus problem


• Thursday, Oct 18
  • Covered in class: PDA to CFG, the pumping lemma for context-free languages


• Homework 6, due Thursday, 10/25, 4:00pm: click here
  

• Slides for this week: Variants of Turing Machines - pdf (ppt), Defining Algorithm - pdf (ppt)


• Tuesday, Oct 23
  • Covered in class: two more non-context-freeness proofs
  • Covered in class: Turing machines (Section 3.1)
  • Covered in class: introduced the class P, and the Halting problem
  • Covered in class: solutions of Hw5


• Thursday, Oct 25
  • Covered in class: Variants of Turing machines (Section 3.2) and The Church-Turing Thesis (Section 3.3)


• Homework 7, due Thursday, 11/1, 4:00pm: click here
  

• Decidable Languages - pdf (ppt), An Undecidable Problem - pdf (ppt), Undecidable problems - pdf (ppt)


• Tuesday, Oct 30
  • Covered in class: Decidable languages (Section 4.1) and the (undecidable) Acceptance problem (Section 4.2)


• Thursday, Nov 1
  • Covered in class: Other undecidable problems / reductions (Section 5.1)


• Homework 8, due Saturday, 11/10, 4:00pm: click here
  Note the later submission deadline - this is due to delayed posting of the homework. You may bring your solutions to class or submit them electronically to the dedicated MyCourses dropbox.

• Slides for this week: Post Correspondence Problem - pdf (ppt), Complexity - pdf (ppt), Classes P and NP - pdf (ppt), NP Completeness - pdf (ppt)


• Tuesday, Nov 6
  • Covered in class: Rice's Theorem (Section 5, Problem 5.28)
  • Covered in class: the Post Correspondence Problem (Section 5.2) and undecidability of ambiguity of a given CFG
  • Covered in class: Measuring complexity - deterministic and nondeterministic (Section 7.1), class P (Section 7.2)
  • Information about the final exam will appear here soon.


• Thursday, Nov 8
  • Covered in class: NP, NP-completeness (Sections 7.3-4)
  • If you are interested in other polynomial-time reductions and NP-complete problems, read Section 7.5.
  • Good luck with your finals!