85 lines
2.2 KiB
TeX
85 lines
2.2 KiB
TeX
\documentclass{article}
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\usepackage{natbib}
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\usepackage{xspace}
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\usepackage{xparse}
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\usepackage{environ}
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\usepackage{hyperref}
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\usepackage{bm}
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\usepackage[english]{babel}
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\usepackage{amsthm}
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\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{mathtools}
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\usepackage{hyperref}
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\usepackage{xfrac}
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\usepackage{stackengine}
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\usepackage[block]{calculation}
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\hypersetup{
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colorlinks=true,
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linkcolor=black,
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filecolor=black,
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urlcolor=black,
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pdfpagemode=FullScreen,
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}
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\input{../notation.tex}
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\input{../glossary.tex}
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\pagenumbering{arabic}
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\pagestyle{plain}
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\newtheorem{theorem}{Theorem}
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\newtheorem{corollary}{Corollary}
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\newtheorem{lemma}{Lemma}
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\newtheorem{proposition}{Proposition}
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\newtheorem{definition}{Definition}
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\newtheorem{example}{Example}
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\newtheorem{remark}{Remark}
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\title{Consistent n-Approximators ($\beta$)}
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\author{}
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\date{}
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\begin{document}
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\maketitle
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\section{Preliminaries}
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\input{sections/preliminaries.tex}
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\section{Sketch Nov 20}
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\input{sections/sketchnov20.tex}
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\section{Sketch Jan 20}
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\input{sections/sketchjan20.tex}
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% iven an \gls{ndao} $o$, its {\em $\beta$-n-stable fixpoints} are fixpoints of the following
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% \begin{align*}
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% B^o_{high}(x) &\define \{ a ~|~ a \in o({x}, a), \neg \exists a',
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% \\ &\hspace{1.5cm}(\boxed{x \preceq_{}}~ a' \prec_{} a) \land (a' \in o({x}, a))) \}\\
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% S(o)(x, y) &\define (C^{o}_{low}(y), B^{o}_{high}(x))
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% \end{align*}}
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% \newcommand{\betastablefixpoint}{\hyperlink{glossary:betastablefixpoint}{$\beta$-stable fixpoint}}
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% \newglossaryentry{betastablefixpoint}{
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% name={$\beta$-stable fixpoint},
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% description={
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% An \gls{interpretation} $(T, P)$ is a {\em $\alpha$-stable fixpoint} (or a $\beta$-stable fixpoint) if it is a \gls{fixpoint} of some $h \in H$ and for each $h' \in H$, none of the following hold
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% \begin{enumerate}[(i.)]
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% \item $\stablerevisionoperator(h')(T, P)_1 \prec_{} T$,
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% \item ($\alpha$-stable only)~$\stablerevisionoperator(h')(T, P)_2 \prec_{} P$, nor
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% \item ($\beta$-stable only) $\exists Z \in \L, T \preceq_{} (h'(T, Z)_2 = Z) \prec_{} P$
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% \end{enumerate}
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% }}
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\bibliographystyle{plain}
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\bibliography{../references}
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\end{document}
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