From: Mart Lubbers Date: Sun, 1 Mar 2015 18:21:59 +0000 (+0100) Subject: dp X-Git-Url: https://git.martlubbers.net/?a=commitdiff_plain;h=dddb01e2bbb4b360cee39610832675d7294d86e4;p=bsc-thesis1415.git dp --- diff --git a/thesis2/3.methods.tex b/thesis2/3.methods.tex index 4fd871d..be8c4b4 100644 --- a/thesis2/3.methods.tex +++ b/thesis2/3.methods.tex @@ -86,11 +86,9 @@ characters from the entry. The first algorithm to generate DAWGs from words was proposed by Hopcroft et al\cite{Hopcroft1971}. It is an incremental approach in generating the graph. Meaning that entry by entry the graph will be expanded. Hopcrofts algorithm has the constraint of lexicographical -ordering. Later on Daciuk et al.\cite{Daciuk2000} improved on the original -algorithm and their algorithm is the algorithm we used to minimize our DAWGs. A -minimal graph is a graph $G$ for which there is no graph $G'$ that has less -paths and $\mathcal{L}(G)=\mathcal{L}(G')$ where $\mathcal{L}(G)$ is the set -of all words present in the DAWG. +ordering. Later on Daciuk et al.\cite{Daciuk1998}\cite{Daciuk2000} improved on +the original algorithm and their algorithm is the algorithm we used to generate +minimal DAWGs from the node lists. \subsection{Algorithm} The algorithm of building DAWGs is an iterative process that goes roughly in @@ -259,5 +257,13 @@ choice. \caption{Example non determinism} \end{figure} -\subsection{How to choose path} +\subsection{Minimality and non-determinism} +The Myhill-Nerode theorem~\cite{Hopcroft1979} states that for every number of +graphs accepting the same language there is a single graph with the least +amount of states. Mihov\cite{Mihov1998} has proven that the algorithm is +minimal in its original form. Our program converts the node-lists to DAWGs that +can possibly contain non deterministic nodes and therefore one can argue about +the minimality. Due to the nature of the determinism this is not the case. 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