% TeX root = main.tex

\newcommand{\V}[0]{\mathcal{V}} % Variables
\newcommand{\PV}[0]{\mathcal{PV}} % Program variables
% \newcommand{\TV}[0]{\mathcal{TV}} % Program variables
\newcommand{\C}[0]{\mathcal{C}} % Set of linear constraints
\newcommand{\D}[0]{\mathcal{D}} % variable distributions 
% \newcommand{\Lin}{\mathcal{LC}} % Set of linear constraints
\newcommand{\PC}{\mathcal{PC}} % Polynomial constraints
\newcommand{\Loc}{\mathcal{L}} % Set of locations
\newcommand{\F}[0]{\mathcal{F}} % Program variables
\newcommand{\Z}[0]{\mathbb{Z}} % whole numbers, integers
\newcommand{\N}[0]{\mathbb{N}} % natural numbers
\newcommand{\R}[0]{\mathbb{R}} % real numbers
\newcommand{\Zs}[0]{\mathfrak{Z}} % the structure of integer arithmetic.
\newcommand{\Rs}[0]{\mathfrak{R}} % the structure of real arithmetic.
\newcommand{\GT}[0]{\mathcal{GT}} % General transitions
\newcommand{\T}[0]{\mathcal{T}} % General transitions
\newcommand{\RB}[0]{\mathcal{RB}} % Runtime bound
\newcommand{\SB}[0]{\mathcal{SB}} % Size bound
\newcommand{\B}[0]{\mathcal{B}} %Bounds
% \newcommand{\Cost}[0]{\mathcal{R}} % Costs
\newcommand{\Cost}[0]{\mathcal{FIXME}} % Costs
\newcommand{\Rt}[0]{\mathcal{R}} %Runtime
\newcommand{\E}[0]{\mathbb{E}} % Expected 
\newcommand{\A}[0]{\mathcal{A}} % Abstract values
\newcommand{\scheduler}[0]{\mathfrak{S}}
\newcommand{\ESs}[0]{\mathbb{E}_{\scheduler,s_0}} % Expected 
\newcommand{\ESns}[0]{\mathbb{E}_{\scheduler',s_0}} % Expected runtime over
% other scheduler
\newcommand{\Prog}[0]{\mathcal{P}} % A PIP
\newcommand{\GRV}[0]{\mathcal{GRV}} % General result variables
\renewcommand{\S}[0]{\mathcal{S}} % grv variable
\newcommand{\RBe}[0]{\mathcal{RB}_\E} % Expected Runtime bound
\newcommand{\SBe}[0]{\mathcal{SB}_\E} % Expected Size bound
\newcommand{\with}[0]{\text{ with }}
\newcommand{\union}[0]{\cup}
\newcommand{\Union}[0]{\bigcup}
\newcommand{\intersect}[0]{\cap}
\newcommand{\Intersect}[0]{\bigcap}
\newcommand{\Land}[0]{\wedge}
\newcommand{\LAnd}[0]{\bigwedge}
\newcommand{\set}[2]{\left\{ #1\hspace{0.5em}|\hspace{0.5em}#2\right\}}
\newcommand{\pathto}[0]{\overset{*}{\rightarrow}}
\newcommand{\npathto}[1]{\overset{#1}{\rightarrow}}
\newcommand{\confs}[0]{\textbf{\textsf{Conf}}}
\newcommand{\runs}[0]{\textbf{\textsf{Runs}}}
\newcommand{\fpath}[0]{\textbf{\textsf{FPath}}}
\newcommand{\unfold}[0]{\mathtt{unfold}}
\newcommand{\evaluate}[0]{\mathtt{evaluate}}
\newcommand{\vers}[0]{\textbf{\textsf{Version}}}
\newcommand{\pr}[0]{\mathit{pr}}
\newcommand{\prSs}[0]{\mathit{pr}_{\scheduler, s_0}}
\newcommand{\prSns}[0]{\mathit{pr}_{\scheduler', s_0}}
\newcommand{\PrSs}[0]{\mathbb{P}_{\scheduler, s_0}}
\newcommand{\PrSns}[0]{\mathbb{P}_{\scheduler', s_0}}
\newcommand{\G}[0]{\mathcal{G}}
\newcommand{\PEG}[0]{\mathcal{G}^\text{PE}}
\newcommand{\TPin}[0]{\T_{\Prog,\mathrm{in}}}
\newcommand{\TPout}[0]{\T_{\Prog,\mathrm{out}}}
\newcommand{\TPnin}[0]{\T_{\Prog',\mathrm{in}}}
\newcommand{\TPnout}[0]{\T_{\Prog',\mathrm{out}}}
\newcommand{\TP}[0]{\mathcal{T}_{\Prog}}
\newcommand{\TPn}[0]{\mathcal{T}_{\Prog'}}
\newcommand{\GTPout}[0]{{\mathcal{G}\mathcal{T}_{\Prog,\mathrm{out}}}}
\newcommand{\GTPnout}[0]{{\mathcal{G}\mathcal{T}_{\Prog',\mathrm{out}}}}
\newcommand{\GTG}[0]{\mathcal{G}\mathcal{T}_\mathrm{G}}
\newcommand{\GTPE}[0]{\mathcal{G}\mathcal{T}_\mathrm{PE}}
\newcommand{\GTP}[0]{\mathcal{G}\mathcal{T}_{\Prog}}
\newcommand{\GTPn}[0]{\mathcal{G}\mathcal{T}_{\Prog'}}
\newcommand{\support}[0]{\mathrm{supp}}
\newcommand{\bigo}[0]{\mathcal{O}}
\newcommand{\MDS}[0]{\Pi^\mathrm{MD}} % Markovian scheduler
\newcommand{\HDS}[0]{\Pi^\mathrm{HD}} % History dependent scheduler
\newcommand{\varf}[0]{\,f\,}
\newcommand{\varff}[0]{\,f}
\newcommand{\varfpi}[1]{\,f\,'\!\!_{#1}}
\newcommand{\ET}[0]{\mathcal{ET}}
\newcommand{\VT}[0]{\mathcal{VT}}
\newcommand{\VTP}[0]{{\mathcal{V}\mathcal{T}_\Prog}}
\newcommand{\simu}[0]{\mathtt{sim}}
\newcommand{\Poly}[0]{\mathcal{H}}
\newcommand{\lift}{\mathord{\uparrow}}
\newcommand{\PRh}[0]{\texttt{PR}_\mathrm{h}}
\newcommand{\PRhv}[0]{\texttt{PR}_\mathrm{hv}}
\newcommand{\PRc}[0]{\texttt{PR}_\mathrm{c}}
\newcommand{\PRcv}[0]{\texttt{PR}_\mathrm{cv}}
\newcommand{\PRd}[0]{\texttt{PR}_\mathrm{d}}
\newcommand{\back}{\texttt{back}}