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18.405J Advanced Complexity Theory (MIT)


This graduate-level course focuses on current research topics in computational complexity theory. Topics include: Nondeterministic, alternating, probabilistic, and parallel computation models; Boolean circuits; Complexity classes and complete sets; The polynomial-time hierarchy; Interactive proof systems; Relativization; Definitions of randomness; Pseudo-randomness and derandomizations;Interactive proof systems and probabilistically checkable proofs.


18.405 | 6.841 | Polynomial hierarchy | time-space lower bounds | approximate counting | ?s Theorem | Relativization | Baker-Gill-Solovay | switching lemma | Razborov-Smolensky | NEXP vs. ACC0 | Communication complexity | PCP theorem | Hadamard code | Gap amplification | Natural proofs


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