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CMU 15-855: Graduate Computational Complexity Theory →0/18
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Lecture 1: Course Introduction and Overview (15-855)

1:20:23
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Lecture 2: Hierarchy Theorems (Time, Space, and Nondeterministic) (15-855)

1:21:06
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Lecture 3: Hopcroft--Paul--Valiant Theorem (15-855)

1:20:29
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Lecture 4: Circuits (15-855)

1:19:50
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Lecture 5: Probabilistic Complexity Classes (15-855)

1:20:55
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Lecture 6: Quasilinear Cook--Levin Theorem (15-855)

1:17:49
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Lecture 7: The Polynomial Time Hierarchy (15-855)

1:19:11
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Lecture 8: Oracles, and the Polynomial Time Hierarchy vs. circuits (15-855)

1:22:04
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Lecture 9: Time/Space Tradeoffs for SAT (15-855)

1:31:30
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Lecture 10: Introduction to Arthur-Merlin classes, MA and AM (15-855)

1:22:37
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Lecture 11: More on constant-round interactive proof systems (15-855)

1:21:18
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Lecture 12: Approximate counting (15-855)

1:19:48
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Lecture 13: Valiant--Vazirani Theorem, and Exact Counting (#P) (15-855)

1:16:15
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Lecture 14: Toda's 1st Theorem and the Permanent (15-855)

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Lecture 20: Permanent is #P-complete (15-855)

1:13:35
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Lecture 15: Algebraic Circuit Complexity (15-855)

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Lecture 16: Instance Checking and the Permanent (15-855)

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Lecture 17: IP = PSPACE (15-855)

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Lecture 20: Permanent is #P-complete (15-855)

Ryan O'DonnellCarnegie Mellon University

Professor

1:13:35·2017·graduate level

A detailed proof establishes that computing the Permanent of a matrix is a #P-complete problem, underscoring its significant computational hardness.

Theory & AlgosComputational ComplexityPermanent#P-completenessCounting Complexity

Graduate Computational Complexity Theory

Lecture 20 (out of order): Permanent is #P-complete

Carnegie Mellon Course 15-855, Fall 2017

Previous · Lecture 14

Lecture 14: Toda's 1st Theorem and the Permanent (15-855)

Next · Lecture 16

Lecture 15: Algebraic Circuit Complexity (15-855)

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