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Diffstat (limited to 'chapters/background/02-interaction-nets.tex')
| -rw-r--r-- | chapters/background/02-interaction-nets.tex | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/chapters/background/02-interaction-nets.tex b/chapters/background/02-interaction-nets.tex index 874110e..41488f1 100644 --- a/chapters/background/02-interaction-nets.tex +++ b/chapters/background/02-interaction-nets.tex @@ -5,7 +5,7 @@ graphical model of computation based on graph rewriting. \subsection{Basic Concepts} -An IN is an undirected graph with labelled vertices, called \textit{agents}. Each agent +An IN is an undirected graph with labeled vertices, called \textit{agents}. Each agent is an instance of a \textit{symbol}, which has a principal port and a fixed number of auxiliary ports: \begin{figure}[H] \centering @@ -21,7 +21,7 @@ is an instance of a \textit{symbol}, which has a principal port and a fixed numb \end{figure} Each port can be wired to at most one other port. When two different agents are wired to their -respective principal ports they are called an \textit{active pair}: +respective principal ports, they are called an \textit{active pair}: \begin{figure}[H] \centering @@ -34,13 +34,13 @@ respective principal ports they are called an \textit{active pair}: \node[left] at (A.above pax 2) {$\mathit{y}$}; \node[right] at (S.above pax) {$\mathit{x}$}; \end{tikzpicture} - \caption{Example of an active pair, where a $\mathit{Add}$ agent and an $\mathit{S}$ agent are connected via their principal ports.} + \caption{Example of an active pair, where an $\mathit{Add}$ agent and an $\mathit{S}$ agent are connected via their principal ports.} \label{fig:active-pair} \end{figure} \subsection{Interaction Rules} Computation in IN proceeds by rewriting the net using local \emph{interaction rules}. A rule -is defined only for an active pair and for any pair of symbols there is at most one +is defined only for an active pair, and for any pair of symbols, there is at most one interaction rule. \begin{figure}[H] @@ -62,12 +62,12 @@ interaction rule. \node[left] at (A.above pax 2) {$\mathit{y}$}; \node[left] at (S.above pal) {$\mathit{z}$}; } - \caption{Interaction rule for $\mathit{S}$ and $\mathit{Add}$ that emulates Peano addition rule.} + \caption{Interaction rule for $\mathit{S}$ and $\mathit{Add}$ that emulates the Peano addition rule.} \label{fig:rule-concrete-zero} \end{figure} \subsection{Properties} -IN possess the following properties: +IN possesses the following properties: \begin{itemize} \item \textbf{Locality}: only active pairs can be rewritten. \item \textbf{Linearity}: each interaction rule rewrites a constant-size subgraph, independent of |