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39
report.tex
39
report.tex
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@ -7,11 +7,13 @@
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\usepackage{graphicx}
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\usepackage{graphicx}
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\usepackage{indentfirst}
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\usepackage{indentfirst}
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\usepackage{enumerate}
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\usepackage{enumerate}
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\usepackage{cite}
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\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
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\usepackage[left=2cm,right=2cm,top=2cm,bottom=2cm]{geometry}
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% Custom packages
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% Custom packages
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\usepackage{leftrule_theorems}
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\usepackage{leftrule_theorems}
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\usepackage{concurgames}
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\usepackage{concurgames}
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\usepackage{symbols}
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\usepackage{my_listings}
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\usepackage{my_listings}
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\usepackage{my_hyperref}
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\usepackage{my_hyperref}
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\usepackage{math}
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\usepackage{math}
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@ -29,6 +31,8 @@
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\todo{abstract}
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\todo{abstract}
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\tableofcontents
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\section{Existing work}
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\section{Existing work}
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My work is set in the context of a wider theory, the basics of which are
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My work is set in the context of a wider theory, the basics of which are
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@ -44,7 +48,8 @@ Opponent plays $B$, thus reaching the configuration $A \cdot B$'').
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\subsection{Event structures}
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\subsection{Event structures}
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\begin{definition}[event structure]
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\begin{definition}[event structure]
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An \emph{event structure} is a pair $(E, \leq_E, \con_E)$, where $E$ is a
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An \emph{event structure}~\cite{winskel1986event} is a pair
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$(E, \leq_E, \con_E)$, where $E$ is a
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set of \emph{events}, $\leq_E$ is a partial order on $E$ and
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set of \emph{events}, $\leq_E$ is a partial order on $E$ and
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$\con_E \subseteq \powerset(E)$ is a set of \emph{consistent events}.
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$\con_E \subseteq \powerset(E)$ is a set of \emph{consistent events}.
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@ -128,7 +133,37 @@ play one of its moves, while~(\ref{def:courteous}) states that unless a
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dependency relation is imposed by the games' rules, one can only make one of
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dependency relation is imposed by the games' rules, one can only make one of
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its moves depend on an Opponent move.
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its moves depend on an Opponent move.
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\section{Implementation of non-concurrent games}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Implementation of deterministic concurrent games}
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\hfill\githubrep[Github repository]{https://github.com/tobast/cam-strategies/}
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\vspace{1em}
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The first part of my internship mostly consisted --- apart from understanding
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the bibliography and the underlying concepts --- in the implementation of
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operations on \emph{deterministic} concurrent games, that is, concurrent games
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as event structures without conflicts. The work had to be done from scratch, as
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no one implemented this before.
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This implementation aims to provide
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\begin{enumerate}[(i)]
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\item a --- more or less --- convenient way to input games/strategies;
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\item basic operations over those games and strategies: parallel
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composition, pullback, interaction, composition, copycat, \ldots;
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\item a clean display as a Dot graph.
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\end{enumerate}
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\subsection{Structures}
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The implementation aims to stay as close as possible to the mathematical model,
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while still providing quite efficient operations.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\bibliography{biblio}
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\bibliographystyle{alpha}
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\end{document}
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\end{document}
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