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
1:13:35Valiant–Vazirani Theorem, and Exact Counting (#P)
Presents the Valiant-Vazirani Theorem, establishing a connection between NP and randomized exact counting (#P), providing insights into counting complexity.
Graduate Computational Complexity Theory Lecture 13: Valiant--Vazirani Theorem, and Exact Counting (#P)