Spring 2004
| CS580 home page | Syllabus | Schedule/Readings | Homework Assignments | Exams and Grading |
| Date | Topics | Readings | HW Assigned | HW Due |
| Tues. 1/13 | Part I: Computability Theory Introduction 3 types of proofs Finite automata Nondeterminism NFA --> DFA |
HU: Ch. 1, 2.1-2.4 | HW 1 | |
| Thur. 1/15 | Closure properties Regular expressions Reg. expr --> FA FA -> Reg. expr. |
HU: Ch. 2.5, part of 3.2 | ||
| Tues. 1/20 | Nonregular languages Regular pumping lemma Context-free languages |
HU: Ch. 3.1, part of 3.4, 4.1-4.5 |
HW 2 | HW 1 |
| Thur. 1/22 | Pushdown Automata CFL --> PDA Context-free pumping lemma |
HU: Ch. 5, 6.1-6.2 | ||
| Tues. 1/27 | ** Come to class to turn in HW2 and pickup HW3. ** No lecture. |
HW 3 | HW 2 | |
| Thur. 1/29* | Turing machines Turing machine variants Church-Turing Thesis |
HU: Ch. 7 | ||
| Tues. 2/3 | Decidability Decidable Languages The Halting problem Diagonalization |
HU: Ch. 8.1-8.3, 3.3, 6.3 |
HW 4 | HW 3 |
| Thur. 2/5 | Rice's Theorem Reducibility Post's Correspondence Problem |
HU: Ch. 8.4-8.6 | ||
| Tues. 2/10 | Post's Correspondence Problem (con't.) Reducibility (con't.) |
HW 4 | ||
| Thur. 2/12 | Exam I, in class | |||
| Tues. 2/17 | Review results from Exam I
Part II: Complexity Theory |
CLR: Ch. 3 |
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| Thur. 2/19 | Time complexity P, NP |
HU: Ch. 12.1-12.2 HU: Ch. 13.1 |
HW 5 | |
| Tues. 2/24 | NP-completeness Polynomial time reducibility NP-complete problems: CLIQUE 3-SAT |
HU: Ch. 13.1-13.2 CLR: Ch. 34.1-34.5 |
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| Thur. 2/26 | Cook-Levin Theorem | HU: Ch. 13.2 CLR: Ch. 34.3 Handout from Sipser text, pgs. 254-259 |
HW 6 | HW 5 |
| Tues. 3/2 | More NP-complete problems: Puzzle Vertex Cover (proof #1) | HU: Ch. 13.2 CLR: Ch. 34.5 |
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| Thur. 3/4 | More NP-complete problems: Vertex Cover (proof #2) Hamiltonian Cycle | HU: Ch. 13.2 CLR: Ch. 34.5 Handout on P and NP Handout from Sipser text, pgs. 262-267 |
HW 7 | HW 6 |
| Tues. 3/9 | No Class (spring break) | |||
| Thur. 3/11 | No Class (spring break) | |||
| Tues. 3/16* | Space Complexity Savitch's Theorem |
HU: Ch. 12.1-12.2, 12.4 | HW 8 | HW 7 |
| Thur. 3/18 | Hierarchy Theorems PSPACE-Complete Quantified Boolean Formulas (QBF) |
HU: Ch. 12.3, 13.4 | ||
| Tues. 3/23 | PSPACE problems: Formula Game Generalized Geography Equiv. RegExp (w/ and w/o expon.) |
Handout from Sipser text, pgs. 287-294 HU: Ch. 13.4, 13.6 (1st section) |
HW 8 | |
| Thur. 3/25 | Exam II, in class | |||
| Tues. 3/30* | Review results from Exam II
Part III: Algorithms (selected topics) Approximation Algorithms: |
CLR: Ch. 35.0-35.1 | HW 9 | |
| Thur. 4/1 | Approximation Algorithms: TSP approx. Set-covering approx. |
CLR: Ch. 35.2-35.3 | ||
| Tues. 4/6 | Approximation Algorithms: Randomization for approx. Subset-sum approx. |
CLR: Ch. 35.4 (1st half) Ch. 35.5 |
HW 10 | HW 9 |
| Thur. 4/8 | Dynamic Programming (Part I) | CLR: Ch. 15.1, 15.3 | ||
| Tues. 4/13 | Dynamic Programming (Part II) | CLR: Ch. 15.2, 15.4 | HW 11 | HW 10 |
| Thur. 4/15 | Greedy Algorithms (Part I) | CLR: Ch. 16.1 - 16.2 | ||
| Tues. 4/20 | Greedy Algorithms (Part II) Computational Geometry (Part I) |
CLR: Ch. 33 | HW 12 | HW 11 |
| Thur. 4/22 | Computational Geometry (Part II) | |||
| Tues. 4/27* | Wrap-Up and Review | HW 12 | ||
| Thur. 5/6 | Exam III, 8-10 AM |
* = TA lecture