$\require{mathtools} % Typesetting \renewcommand{\th}{^{\mathrm{th}}} \renewcommand{\degree}{^\circ} % Delimiters \DeclarePairedDelimiter{\floor}{\lfloor}{\rfloor} \DeclarePairedDelimiter{\ceil}{\lceil}{\rceil} \DeclarePairedDelimiter{\inner}{\langle}{\rangle} \DeclarePairedDelimiter{\set}{\{}{\}} \DeclarePairedDelimiter{\p}{(}{)} \DeclarePairedDelimiter{\sqb}{[}{]} \let\b\undefined \DeclarePairedDelimiter{\b}{[}{]} \DeclarePairedDelimiter{\abs}{|}{|} \DeclarePairedDelimiter{\norm}{\|}{\|} % Sets \newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\R}{\mathbb{R}} \newcommand{\F}{\mathbb{F}} % Miscellaneous \DeclareMathOperator{\poly}{poly} \DeclareMathOperator{\polylog}{polylog} \DeclareMathOperator{\negl}{negl} \DeclareMathOperator{\median}{median} \DeclareMathOperator{\One}{\mathbf{1}} \DeclareMathOperator{\1}{\mathbf{1}} \DeclareMathOperator{\LHS}{LHS} \DeclareMathOperator{\RHS}{RHS} \DeclareMathOperator{\argmin}{arg\,min} \DeclareMathOperator{\argmax}{arg\,max} \newcommand{\heart}{\heartsuit} \newcommand{\eps}{\epsilon} \DeclareMathOperator{\span}{span} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator{\Ima}{Im} \newcommand{\transp}{\mathsf{T}} % Shortcuts & aliases \newcommand{\sse}{\subseteq} \newcommand{\ce}{\coloneqq} \newcommand{\ec}{\eqqcolon} \newcommand{\al}[1]{\begin{align}#1\end{align}} \newcommand{\ob}{\overbrace} \newcommand{\ub}{\underbrace} \newcommand{\and}{\wedge} \newcommand{\AND}{\bigwedge} \newcommand{\or}{\vee} \newcommand{\OR}{\bigvee} \newcommand{\xor}{\oplus} \newcommand{\XOR}{\bigoplus} \newcommand{\union}{\cup} \newcommand{\inter}{\cap} \newcommand{\comp}{\overline} % Classes \newcommand{\co}{\mathsf{co}} \newcommand{\Prom}{\mathsf{Promise}} \newcommand{\P}{\mathsf{P}} \newcommand{\NP}{\mathsf{NP}} \newcommand{\PH}{\mathsf{PH}} \newcommand{\PSPACE}{\mathsf{PSPACE}} \newcommand{\L}{\mathsf{L}} \newcommand{\formost}{\mathsf{Я}} \newcommand{\RP}{\mathsf{RP}} \newcommand{\BPP}{\mathsf{BPP}} \newcommand{\MA}{\mathsf{MA}} \newcommand{\AM}{\mathsf{AM}} \newcommand{\IP}{\mathsf{IP}} \newcommand{\RL}{\mathsf{RL}} \newcommand{\NC}{\mathsf{NC}} \newcommand{\AC}{\mathsf{AC}} \newcommand{\ACC}{\mathsf{ACC}} \newcommand{\TC}{\mathsf{TC}} \newcommand{\Ppoly}{\mathsf{P}/\!\poly} \newcommand{\Lpoly}{\mathsf{L}/\!\poly} \newcommand{\TIME}{\mathsf{TIME}} \newcommand{\SPACE}{\mathsf{SPACE}} \newcommand{\TISP}{\mathsf{TISP}} \newcommand{\SIZE}{\mathsf{SIZE}} % Probability \newcommand{\Normal}{\mathcal{N}} \let\Pr\undefined \DeclareMathOperator{\Pr}{\mathbf{Pr}} \DeclareMathOperator{\E}{\mathbf{E}} \DeclareMathOperator{\Var}{\mathbf{Var}} \DeclareMathOperator{\dTV}{d_{\mathrm{TV}}} \DeclareMathOperator{\corr}{\mathrm{corr}} \let\H\undefined \DeclareMathOperator{\H}{\mathbf{H}} \DeclareMathOperator{\I}{\mathbf{I}} % Boolean analysis \newcommand{\zo}{\set{0,1}} \newcommand{\pmo}{\set{\pm 1}} \newcommand{\harpoon}{\!\upharpoonright\!} \newcommand{\restrict}[2]{#1\harpoon_{#2}} % deprecated \newcommand{\rr}[2]{#1\harpoon_{#2}} \newcommand{\Fou}[1]{\widehat{#1}} \DeclareMathOperator{\Ind}{\mathrm{Ind}} \DeclareMathOperator{\Inf}{\mathrm{Inf}} \DeclareMathOperator{\Stab}{\mathrm{Stab}} \DeclareMathOperator{\T}{T} \DeclareMathOperator{\sens}{\mathrm{s}} \DeclareMathOperator{\bsens}{\mathrm{bs}} \DeclareMathOperator{\fbsens}{\mathrm{fbs}} \DeclareMathOperator{\Cert}{\mathrm{C}} \DeclareMathOperator{\DT}{\mathrm{DT}} \DeclareMathOperator{\CDT}{\mathrm{CDT}} % canonical \DeclareMathOperator{\ECDT}{\mathrm{ECDT}} % canonical \DeclareMathOperator{\AvgDT}{\mathrm{AvgDT}} \DeclareMathOperator{\PDT}{\mathrm{PDT}} % partial decision tree \DeclareMathOperator{\DTsize}{\mathrm{DT_{size}}} \DeclareMathOperator{\W}{\mathbf{W}} % Functions (small caps sadly doesn't work) \DeclareMathOperator{\Par}{\mathrm{Par}} \DeclareMathOperator{\Maj}{\mathrm{Maj}} \DeclareMathOperator{\HW}{\mathrm{HW}} \DeclareMathOperator{\Th}{\mathrm{Th}} \DeclareMathOperator{\Tribes}{\mathrm{Tribes}} \DeclareMathOperator{\RotTribes}{\mathrm{RotTribes}} \DeclareMathOperator{\CycleRun}{\mathrm{CycleRun}} \DeclareMathOperator{\SAT}{\mathrm{SAT}} \DeclareMathOperator{\UniqueSAT}{\mathrm{UniqueSAT}} % Alignment \DeclareMathOperator{\Amp}{\mathrm{Amp}} % Calligraphy \newcommand{\calA}{\mathcal{A}} \newcommand{\calB}{\mathcal{B}} \newcommand{\calC}{\mathcal{C}} \newcommand{\calD}{\mathcal{D}} \newcommand{\calE}{\mathcal{E}} \newcommand{\calF}{\mathcal{F}} \newcommand{\calG}{\mathcal{G}} \newcommand{\calH}{\mathcal{H}} \newcommand{\calI}{\mathcal{I}} \newcommand{\calJ}{\mathcal{J}} \newcommand{\calK}{\mathcal{K}} \newcommand{\calL}{\mathcal{L}} \newcommand{\calM}{\mathcal{M}} \newcommand{\calN}{\mathcal{N}} \newcommand{\calO}{\mathcal{O}} \newcommand{\calP}{\mathcal{P}} \newcommand{\calQ}{\mathcal{Q}} \newcommand{\calR}{\mathcal{R}} \newcommand{\calS}{\mathcal{S}} \newcommand{\calT}{\mathcal{T}} \newcommand{\calU}{\mathcal{U}} \newcommand{\calV}{\mathcal{V}} \newcommand{\calW}{\mathcal{W}} \newcommand{\calX}{\mathcal{X}} \newcommand{\calY}{\mathcal{Y}} \newcommand{\calZ}{\mathcal{Z}} % Bold \newcommand{\bA}{\boldsymbol{A}} \newcommand{\bB}{\boldsymbol{B}} \newcommand{\bC}{\boldsymbol{C}} \newcommand{\bD}{\boldsymbol{D}} \newcommand{\bE}{\boldsymbol{E}} \newcommand{\bF}{\boldsymbol{F}} \newcommand{\bG}{\boldsymbol{G}} \newcommand{\bH}{\boldsymbol{H}} \newcommand{\bI}{\boldsymbol{I}} \newcommand{\bJ}{\boldsymbol{J}} \newcommand{\bK}{\boldsymbol{K}} \newcommand{\bL}{\boldsymbol{L}} \newcommand{\bM}{\boldsymbol{M}} \newcommand{\bN}{\boldsymbol{N}} \newcommand{\bO}{\boldsymbol{O}} \newcommand{\bP}{\boldsymbol{P}} \newcommand{\bQ}{\boldsymbol{Q}} \newcommand{\bR}{\boldsymbol{R}} \newcommand{\bS}{\boldsymbol{S}} \newcommand{\bT}{\boldsymbol{T}} \newcommand{\bU}{\boldsymbol{U}} \newcommand{\bV}{\boldsymbol{V}} \newcommand{\bW}{\boldsymbol{W}} \newcommand{\bX}{\boldsymbol{X}} \newcommand{\bY}{\boldsymbol{Y}} \newcommand{\bZ}{\boldsymbol{Z}} \newcommand{\ba}{\boldsymbol{a}} \newcommand{\bb}{\boldsymbol{b}} \newcommand{\bc}{\boldsymbol{c}} \newcommand{\bd}{\boldsymbol{d}} \newcommand{\be}{\boldsymbol{e}} \renewcommand{\bf}{\boldsymbol{f}} \newcommand{\bg}{\boldsymbol{g}} \newcommand{\bh}{\boldsymbol{h}} \newcommand{\bi}{\boldsymbol{i}} \newcommand{\bj}{\boldsymbol{j}} \newcommand{\bk}{\boldsymbol{k}} \newcommand{\bp}{\boldsymbol{p}} \newcommand{\bq}{\boldsymbol{q}} \newcommand{\br}{\boldsymbol{r}} \newcommand{\bs}{\boldsymbol{s}} \newcommand{\bt}{\boldsymbol{t}} \newcommand{\bu}{\boldsymbol{u}} \newcommand{\bv}{\boldsymbol{v}} \newcommand{\bw}{\boldsymbol{w}} \newcommand{\bx}{\boldsymbol{x}} \newcommand{\by}{\boldsymbol{y}} \newcommand{\bz}{\boldsymbol{z}}$

Facts

Discrete

Conceptual