dp

diff --git a/thesis2/3.methods.tex b/thesis2/3.methods.tex
index 4fd871d..be8c4b4 100644 (file)
--- 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. The
+non determinism is only visible when matching the data and not in the real
+graph since in the real graph we ...
 

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diff --git a/thesis2/thesis.bib b/thesis2/thesis.bib
index 0b54b2a..50f34c6 100644 (file)
--- a/thesis2/thesis.bib
+++ b/thesis2/thesis.bib
@@ -180,3 +180,27 @@ title = {{Constructing minimal acyclic deterministic finite automata}}
        volume = {40},
        year = {1985}
 }
+@book{Hopcroft1979,
+       title={Introduction to automata theory, languages, and computation},
+       author={Hopcroft, John E},
+       year={1979},
+       publisher={Pearson Education India}
+}
+@article{Mihov1998,
+       author = {Mihov, Stoyan},
+       pages = {1--6},
+       year={1998},
+       title = {{Direct Building of Minimal Automaton for Given List 2 Formal
+               background and notations 3 Method description}}
+}
+@inproceedings{Daciuk1998,
+       title={Incremental construction of minimal acyclic finite state
+               automata and transducers},
+       author={Daciuk, Jan and Watson, Bruce W and Watson, Richard E},
+       booktitle={Proceedings of the International Workshop on Finite
+               State Methods in Natural Language Processing},
+       pages={48--56},
+       year={1998},
+       organization={Association for Computational Linguistics}
+}
+