Css 203 1 Computational Complexity Lecture 29

Summary

Agenda: PCP Theorem(s) and applications to inapproximability results Instructor: Prahladh Harsha. Agenda: Hardness of approximating clique (FGLSS reduction), PCPs and more Instructor: Prahladh Harsha. Agenda: decision vs counting; of of Permanent. Instructor: Ramprasad Saptharishi. Agenda: Arthur-Merlin protocols, MA, AM, properties of AM protocols, GI - NP-complete? public coins = private coins. Instructor: ... Agenda: Savitch's theorem; logspace reductions; L, NL, coNL, complete problems and relationships Instructor: Prahladh Harsha. Agenda: IP ⊂ PSPACE; P^ ⊂ IP (via extension to TQBF; IP = PSPACE Instructor: Prahladh Harsha. Agenda: Immerman–Szelepcsényi theorem; introduction to the polynomial hierarchy (definition via quantifiers and oracles) ... Agenda: Toda's theorem: intro. to ⊕SAT, randomised reduction from PH to ⊕SAT, derandomisation via a query Instructor: ... Agenda: Conclusion - What we saw and didn't see in this course Instructor: Ramprasad Saptharishi. Agenda: Multiprover interactive proofs (MIP), MIP=NEXP, Introduction to PCPs, The PCP Theorem Instructor: Prahladh Harsha. Agenda: Universal TM simulation, Classes P and NP, non-determinisim, polynomial Agenda: What is a proof?; Graph non-isomorphism; Interactive Proofs (formal definition); what we can prove; an interactive proof ... Agenda: Razborov and Smolensky's proof that Parity is not in AC0 Instructor: Ramprasad Saptharishi.