Css 203 1 Computational Complexity Lecture 13

Summary

Agenda: TBA Instructor: Prahladh Harsha. Agenda: Administrivia; problems of interest: GCD, primality, connectivity, matching, determinant, SAT, CNF-minimization, ... Agenda: Karp-Lipton and Meyer's theorem; Size hierarchy theorem; Turing Machines with advice; some important circuit classes ... Agenda: Cook-Levin Theorem, web of reductions, decision vs. search, downward self-reducibility of SAT. Agenda: Immerman–Szelepcsényi theorem; introduction to the polynomial hierarchy (definition via quantifiers and oracles) ... Agenda: Polynomial hierarchy via oracle TMs; alternating TMs and classes; towards Here, the great Yuri Gurevich, mathematician, Agenda: IP ⊂ PSPACE; P^ ⊂ IP (via extension to TQBF; IP = PSPACE Instructor: Prahladh Harsha. Agenda: decision vs counting; of of Permanent. Instructor: Ramprasad Saptharishi. Agenda: Approximate counting with an NP oracle; self-reducibility properties of the Permanent Instructor: Ramprasad Saptharishi. Agenda: Toda's theorem: intro. to ⊕SAT, randomised reduction from PH to ⊕SAT, derandomisation via a query Instructor: ...