Course Introduction and Overview
1:20:23Hierarchy Theorems (Time, Space, and Nondeterministic)
1:21:06Hopcroft--Paul--Valiant Theorem
1:20:29Circuits
1:19:50Probabilistic Complexity Classes
1:20:55Quasilinear Cook--Levin Theorem
1:17:49The Polynomial Time Hierarchy
1:19:11Oracles, and the Polynomial Time Hierarchy vs. circuits
1:22:04Time/Space Tradeoffs for SAT
1:31:30Introduction to Arthur-Merlin classes, MA and AM
1:22:37More on constant-round interactive proof systems
1:21:18Approximate counting
1:19:48Valiant--Vazirani Theorem, and Exact Counting (#P)
1:16:15Toda's 1st Theorem and the Permanent
1:18:15Algebraic Circuit Complexity
1:20:29Instance Checking and the Permanent
1:20:19IP = PSPACE
1:18:47Permanent is #P-complete
1:13:35Hopcroft--Paul--Valiant Theorem
Focuses on the Hopcroft Paul Valiant Theorem, examining its implications for efficient simulation of multi-tape Turing machines by single-tape machines.
Graduate Computational Complexity Theory
Lecture 3: Hopcroft--Paul--Valiant Theorem
Carnegie Mellon Course 15-855, Fall 2017