Lecture 1: Course Introduction and Overview (15-855)
1:20:23Lecture 2: Hierarchy Theorems (Time, Space, and Nondeterministic) (15-855)
1:21:06Lecture 3: Hopcroft--Paul--Valiant Theorem (15-855)
1:20:29Lecture 4: Circuits (15-855)
1:19:50Lecture 5: Probabilistic Complexity Classes (15-855)
1:20:55Lecture 6: Quasilinear Cook--Levin Theorem (15-855)
1:17:49Lecture 7: The Polynomial Time Hierarchy (15-855)
1:19:11Lecture 8: Oracles, and the Polynomial Time Hierarchy vs. circuits (15-855)
1:22:04Lecture 9: Time/Space Tradeoffs for SAT (15-855)
1:31:30Lecture 10: Introduction to Arthur-Merlin classes, MA and AM (15-855)
1:22:37Lecture 11: More on constant-round interactive proof systems (15-855)
1:21:18Lecture 12: Approximate counting (15-855)
1:19:48Lecture 13: Valiant--Vazirani Theorem, and Exact Counting (#P) (15-855)
1:16:15Lecture 14: Toda's 1st Theorem and the Permanent (15-855)
1:18:15Lecture 20: Permanent is #P-complete (15-855)
1:13:35Lecture 15: Algebraic Circuit Complexity (15-855)
1:20:29Lecture 16: Instance Checking and the Permanent (15-855)
1:20:19Lecture 17: IP = PSPACE (15-855)
1:18:47Lecture 2: Hierarchy Theorems (Time, Space, and Nondeterministic) (15-855)
This session delves into the Hierarchy Theorems, establishing distinct complexity classes based on time, space, and nondeterministic resource bounds as detailed in Arora-Barak.
Graduate Computational Complexity Theory
Lecture 2: Hierarchy Theorems (Time, Space, and Nondeterministic)
Carnegie Mellon Course 15-855, Fall 2017
Lecture 1: Course Introduction and Overview (15-855)
Next · Lecture 3Lecture 3: Hopcroft--Paul--Valiant Theorem (15-855)