This course is taught using Professor Sipser’s textbook:
Sipser, Michael. Introduction to the Theory of Computation. 3rd ed. Cengage Learning, 2012. ISBN: 9781133187790.
We will cover Chapters 1, 2 (except 2.4), 3, 4, 5, 6.1, 7, 8, 9.1, 9.2, 10.2 (except the part on Primality), and 10.4 through Theorem 10.33.
| LEC # | TOPICS | READINGS |
|---|---|---|
| 1 | Introduction, Finite Automata, Regular Expressions | Section 1.1 |
| 2 | Nondeterminism, Closure Properties, Regular Expressions → Finite Automata | Sections 1.2 and 1.3 |
| 3 | The Regular Pumping Lemma, Finite Automata → Regular Expressions, CFGs | Sections 1.4, 2.0, and 2.1 |
| 4 | Pushdown Automata, CFG ↔ PDA | Section 2.2 |
| 5 | The CF Pumping Lemma, Turing Machines | Sections 2.3 and 3.1 |
| 6 | TM Variants, the Church-Turing Thesis | Sections 3.2 and 3.3 |
| 7 | Decision Problems for Automata and Grammars | Section 4.1 |
| 8 | Undecidability | Section 4.2 |
| 9 | Reducibility | Section 5.1 |
| 10 | The Computation History Method | Section 5.2 |
| 11 | The Recursion Theorem and Logic | Sections 6.1 and 6.2 |
| 12 | Time Complexity | Section 7.1 |
| 13 | Midterm Exam | [no readings] |
| 14 | P and NP, SAT, Poly-time Reducibility | Sections 7.2 and 7.3 |
| 15 | NP-Completeness | Section 7.5 |
| 16 | Cook-Levin Theorem | Section 7.4 |
| 17 | Space Complexity, PSPACE, Savitch’s Theorem | Sections 8.1 and 8.2 |
| 18 | PSPACE-Completeness | Section 8.3 |
| 19 | Games, Generalized Geography | Section 8.3 |
| 20 | L and NL, NL = coNL | Section 8.4 |
| 21 | Hierarchy Theorems | Section 9.1 |
| 22 | Provably Intractable Problems, Oracles | Section 9.2 |
| 23 | Probabilistic Computation, BPP | Section 10.2 |
| 24 | Probabilistic Computation (cont.) | Section 10.2 |
| 25 | Interactive Proof Systems, IP | Section 10.4 |
| 26 | coNP ⊆ IP | Section 10.4 |
