For some lectures we will follow
Lectures in Computational Complexity
of Jin-Yi Cai (LC below), the book
Computational Complexity: A Modern Approach
of Sanjeev Arora and Boaz Barak (MA below), and the book
Communication Complexity
of Anup Rao and Amir Yehudayoff (CC below). TC denotes the Sipser book
Test days: we will have the test the first 50 mins of class so pleasea come on time!
Date |
Topic |
Readings |
HW/Practice Probs |
|
|---|---|---|---|---|
| Sep 11 | Introduction; Review: Turing machines, Time Complexity, P vs NP, NP-Completeness | Notes; TC 3.1-3.2, and 7; LC 2.1-2.2 | ||
| Sep 18 | Polynomial Hierarchy; Hierarchy theorems, Space Complexity | Notes; TC 7 and 9.1, LC 2.3-2.5 | ||
| Sep 25 | Space Complexity: Classes L, NL, PSPACE; NL=coNL; PSPACE=NPSPACE | Notes; TC Chap 8; LC Chap 3, MA Chap 4) | HW1 OUT 9/23; DUE 10/01m | |
| Oct 2 | Space Complexity cont'd: Catalytic Space, Cook-Mertz and Williams' | Notes; Simulating time in sqrt-space (Williams) | Test 1 Practice Probs | |
| Oct 9 | Test 1; Intro to Randomization: RP, BPP, examples | Probability Basics; LC 5.1, 5.4-5.5; MA Ch 7. | HW2 OUT 10/7; DUE 10/15 | |
| Oct 16 | Randomization cont'd: hardness vs. randomness; randomness in cryptography | LC 5.1, 5.4-5.5; MA Ch 7. | ||
| Oct 23 | Test 2; Interactive Proofs; #SAT in IP, IP=PSPACE | TC Sec 10.4; MA Ch 8. | ||
| Oct 30 | Approximation Algs, PCP Theorem. | MA Sec 18-1-18.2 | HW3 OUT 11/2; DUE 11/12 | |
| Nov 6 | Intro Communication Complexity, Deterministic, Randomized CC | CC pp. 15-37 | ||
| Nov 13 | Communication Complexity cont'd, Lower Bounds, Set Disjointness | CC Chap 3; Sec 2 of Notes (S. Lovett) | ||
| Nov 20 | Test 3; Intro Circuit Complexity | LC Sec 4.1-4.2; MA Ch 6. | ||
| Nov 27 | Holiday (no class) | HW4 OUT 11/30; DUE 12/10 | ||
| Dec 4 | Circuit Complexity cont'd. | |||
| Dec 11 | (Last Class) TFNP and proof complexity, Wrap-up | CC pp. 97-101 | ||
| Dec 18 | Final Exam (See Exam Schedule for Time/Location) |