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Permanent is #P-complete: Graduate Complexity Lecture 20 (out of order) at CMU
Valiant--Vazirani Theorem, and Exact Counting (#P): Graduate Complexity Lecture 13 at CMU
Random Restrictions and AC0 Circuit Lower Bounds: Graduate Complexity Lecture 18 at CMU
Hardness amplification: Graduate Complexity Lecture 26 at CMU
Time/Space Tradeoffs for SAT: Graduate Complexity Lecture 9 at CMU
Hardness vs. Randomness II: Graduate Complexity Lecture 25 at CMU
Undergrad Complexity at CMU - Lecture 27: Hardness within P
Hopcroft--Paul--Valiant Theorem: Graduate Complexity Lecture 3 at CMU
Hardness vs. Randomness I: Graduate Complexity Lecture 24 at CMU
Algebraic Circuit Complexity: Graduate Complexity Lecture 15 at CMU
Algebraic NP vs. P vs. Boolean NP vs. P: Graduate Complexity Lecture 15 postscript at CMU
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Last Updated: September 16, 2026
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