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Fix few sentences starting with math.

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Théophile Bastian 2016-08-21 00:41:37 +02:00
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report.tex
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@ -473,11 +473,12 @@ The ESP of the previous example would then be
\vspace{-0.5em} \vspace{-0.5em}
\[ {\forall x \in X}, {\forall e \in A}, {e \leq_A x} \implies {e \in X}.\] \[ {\forall x \in X}, {\forall e \in A}, {e \leq_A x} \implies {e \in X}.\]
$\config(A)$ is the set of configurations of $A$. We write $\config(A)$ the set of configurations of $A$.
\end{definition} \end{definition}
A configuration can thus be seen as a valid state of the game. $\config(A)$ A configuration can thus be seen as a valid state of the game. The set
plays a major role in definitions and proofs on games and strategies. $\config(A)$ plays a major role in definitions and proofs on games and
strategies.
\begin{notation} \begin{notation}
For $x,y \in \config(A)$, $x \forkover{e} y$ states that $y = For $x,y \in \config(A)$, $x \forkover{e} y$ states that $y =
@ -713,10 +714,10 @@ adding ``neutral'' states for $A$ and $C$, which gives us two strategies
playing on the same game (if we ignore polarities), $A \parallel B \parallel playing on the same game (if we ignore polarities), $A \parallel B \parallel
C$. C$.
$\tau \strInteract \sigma$ is an \emph{event structure} (\ie, without Here, we define $\tau \strInteract \sigma$ as an \emph{event structure} (\ie,
polarities): indeed, the two strategies disagree on the polarities of the without polarities): indeed, the two strategies disagree on the polarities of
middle part. Alternatively, it can be seen as an ESP with a polarity function the middle part. Alternatively, it can be seen as an ESP with a polarity
over $\set{+,-,?}$. function over $\set{+,-,?}$.
From this point, the notion of composition we sought is only a matter of From this point, the notion of composition we sought is only a matter of
``hiding'' the middle part: ``hiding'' the middle part:
@ -1027,7 +1028,7 @@ can compute its associated strategy and check whether it is $\seman{1}$.
\vspace{1em} \vspace{1em}
One of the objectives of my internship was also to implement the operations on One of the goals of my internship was also to implement the operations on
games and strategies described in §\ref{sssec:es_operations}, and to use them games and strategies described in §\ref{sssec:es_operations}, and to use them
to provide a convenient Dot representation of the operational semantics of to provide a convenient Dot representation of the operational semantics of
\llccs{} described in §\ref{ssec:llccs_interp}. \llccs{} described in §\ref{ssec:llccs_interp}.