$
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\notag
$
$
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\newcommand{\sgeq}{\ensuremath{\succeq}}
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\notag
$
$
\newcommand{\transpose}[1]{\ensuremath{#1{}^{\mkern-2mu\intercal}}}
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\notag
$
$
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\notag
$
$
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\newcommand\prRP{\class{prRP}}
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\newcommand{\PSPACE}{\class{PSPACE}}
\newcommand{\NSPACE}{\class{NSPACE}}
\newcommand{\coNSPACE}{\coclass{NSPACE}}
\newcommand{\coL}{\coclass{L}}
\newcommand{\coP}{\coclass{P}}
\newcommand{\coNP}{\coclass{NP}}
\newcommand{\coNL}{\coclass{NL}}
\newcommand{\coNPSPACE}{\coclass{NPSPACE}}
\newcommand{\APSPACE}{\class{APSPACE}}
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\newcommand{\SigmaTIME}[1]{\class{\Sigma_{#1}TIME}}
\newcommand{\PiTIME}[1]{\class{\Pi_{#1}TIME}}
\newcommand{\SigmaP}[1]{\class{\Sigma_{#1}P}}
\newcommand{\PiP}[1]{\class{\Pi_{#1}P}}
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\newcommand{\ATIME}{\class{ATIME}}
\newcommand{\ASPACE}{\class{ASPACE}}
\newcommand{\AP}{\class{AP}}
\newcommand{\AL}{\class{AL}}
\newcommand{\APSPACE}{\class{APSPACE}}
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\newcommand{\NC}[1]{\class{NC^{#1}}}
\newcommand{\AC}[1]{\class{AC^{#1}}}
\newcommand{\ACC}[1]{\class{ACC^{#1}}}
\newcommand{\TC}[1]{\class{TC^{#1}}}
\newcommand{\ShP}{\class{\# P}}
\newcommand{\PaP}{\class{\oplus P}}
\newcommand{\PCP}{\class{PCP}}
\newcommand{\kMIP}[1]{\class{#1\mbox{-}MIP}}
\newcommand{\MIP}{\class{MIP}}
$
$
\newcommand{\textprob}[1]{\text{#1}}
\newcommand{\mathprob}[1]{\textbf{#1}}
\newcommand{\Satisfiability}{\textprob{Satisfiability}}
\newcommand{\SAT}{\textprob{SAT}}
\newcommand{\TSAT}{\textprob{3SAT}}
\newcommand{\USAT}{\textprob{USAT}}
\newcommand{\UNSAT}{\textprob{UNSAT}}
\newcommand{\QPSAT}{\textprob{QPSAT}}
\newcommand{\TQBF}{\textprob{TQBF}}
\newcommand{\LinProg}{\textprob{Linear Programming}}
\newcommand{\LP}{\mathprob{LP}}
\newcommand{\Factor}{\textprob{Factoring}}
\newcommand{\CircVal}{\textprob{Circuit Value}}
\newcommand{\CVAL}{\mathprob{CVAL}}
\newcommand{\CircSat}{\textprob{Circuit Satisfiability}}
\newcommand{\CSAT}{\textprob{CSAT}}
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\newcommand{\MonCircVal}{\textprob{Monotone Circuit Value}}
\newcommand{\Reachability}{\textprob{Reachability}}
\newcommand{\Unreachability}{\textprob{Unreachability}}
\newcommand{\RCH}{\mathprob{RCH}}
\newcommand{\BddHalt}{\textprob{Bounded Halting}}
\newcommand{\BH}{\mathprob{BH}}
\newcommand{\DiscreteLog}{\textprob{Discrete Log}}
\newcommand{\REE}{\mathprob{REE}}
\newcommand{\QBF}{\mathprob{QBF}}
\newcommand{\MCSP}{\mathprob{MCSP}}
\newcommand{\GGEO}{\mathprob{GGEO}}
\newcommand{\CKTMIN}{\mathprob{CKT-MIN}}
\newcommand{\MINCKT}{\mathprob{MIN-CKT}}
\newcommand{\IdentityTest}{\textprob{Identity Testing}}
\newcommand{\Majority}{\textprob{Majority}}
\newcommand{\CountIndSets}{\textprob{\#Independent Sets}}
\newcommand{\Parity}{\textprob{Parity}}
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\newcommand{\CountCycles}{\textprob{#Cycles}}
\newcommand{\CountPerfMatchings}{\textprob{\#Perfect Matchings}}
\newcommand{\CountMatchings}{\textprob{\#Matchings}}
\newcommand{\CountMatch}{\mathprob{\#Matchings}}
\newcommand{\ECSAT}{\mathprob{E#SAT}}
\newcommand{\ShSAT}{\mathprob{#SAT}}
\newcommand{\ShTSAT}{\mathprob{#3SAT}}
\newcommand{\HamCycle}{\textprob{Hamiltonian Cycle}}
\newcommand{\Permanent}{\textprob{Permanent}}
\newcommand{\ModPermanent}{\textprob{Modular Permanent}}
\newcommand{\GraphNoniso}{\textprob{Graph Nonisomorphism}}
\newcommand{\GI}{\mathprob{GI}}
\newcommand{\GNI}{\mathprob{GNI}}
\newcommand{\GraphIso}{\textprob{Graph Isomorphism}}
\newcommand{\QuantBoolForm}{\textprob{Quantified Boolean
Formulae}}
\newcommand{\GenGeography}{\textprob{Generalized Geography}}
\newcommand{\MAXTSAT}{\mathprob{Max3SAT}}
\newcommand{\GapMaxTSAT}{\mathprob{GapMax3SAT}}
\newcommand{\ELIN}{\mathprob{E3LIN2}}
\newcommand{\CSP}{\mathprob{CSP}}
\newcommand{\Lin}{\mathprob{Lin}}
\newcommand{\ONE}{\mathbf{ONE}}
\newcommand{\ZERO}{\mathbf{ZERO}}
\newcommand{\yes}
\newcommand{\no}
$
Notes
I like to record what I had learned from classes, heard from talks, or even seen on other blogs in a casual style. Unlike my othere blog posts, the notes here will be more technical and not meant for general audience. If you find any mistakes or feel confused, please let me know! Also, I procrastinate a lot so please forgive me on being incomplete in many notes.
Categories
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