Exploring Noc21 Cs49 Lec04

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  • the proof by Razborov and Smolensky.
  • The circuit classes NC and AC. The relation between the various levels of the NC and AC hierarchy. Parity is in NC1.
  • Lower bounding the communication complexity of a function using the tiling method.
  • Completed the hardness proof of permanent. Interactive proofs. Interactive proof with a deterministic verifier is same as NP.
  • Completed proof of Immerman-Szelepscenyi Theorem. The Polynomial Hierarchy - motivation for studying, definition.

In-Depth Information on Noc21 Cs49 Lec04

Proved that directed Hamiltonian path problem is NP-complete. The class coNP. Complete problem (SAT). Discussed why ... The two views of considering the PCP Theorem -- as a locally and probabilistically checkable proof system, and as a hardness ... Properties of logspace reductions such as transitivity, closure of L under such reductions. Path is NL-complete. Valiant-Vazirani Theorem for USAT. Definition of the classes #P and ⊕P. #SAT is complete for #P. Closure of the ⊕ quantifier ...

Parity not in AC0 - II.

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