From a3a6397bfd8a80bc49374ba168d8b8437c5de8a0 Mon Sep 17 00:00:00 2001
From: Camil Staps
Date: Mon, 23 Oct 2017 14:24:06 +0200
Subject: Add hypotheses

---
 assignments/assignment2/assignment2.tex | 50 +++++++++++++++++++++++++--------
 1 file changed, 38 insertions(+), 12 deletions(-)

(limited to 'assignments/assignment2/assignment2.tex')

diff --git a/assignments/assignment2/assignment2.tex b/assignments/assignment2/assignment2.tex
index 26e964e..655179b 100644
--- a/assignments/assignment2/assignment2.tex
+++ b/assignments/assignment2/assignment2.tex
@@ -7,6 +7,7 @@
 \usepackage{graphicx}
 \usepackage{caption}
 \usepackage{cleveref}
+\usepackage{subfig}
 
 \let\oldurl\url
 \def\url#1{{\small\oldurl{#1}}}
@@ -44,23 +45,22 @@
 			\item 10ct 10ct 10ct 10ct 10ct snickers snickers
 			\item 10ct 10ct 10ct snickers 10ct twix
 			\item 10ct 10ct 10ct 5ct snickers twix
+			\item 10ct 10ct 5ct 10ct snickers mars
+			\item 10ct 10ct 5ct 10ct 10ct mars mars snickers
 		\end{itemize}
 
 		The hypotheses are given in \cref{fig:lstar-run} (p.~\pageref{fig:lstar-run}).
 
-		\begin{figure}[p]
-			\includegraphics[width=.5\textwidth]{LStar_hypothesis0}
-			\includegraphics[width=.5\textwidth]{LStar_hypothesis1}
-			\includegraphics[width=.5\textwidth]{LStar_hypothesis2}
-			\includegraphics[width=.5\textwidth]{LStar_hypothesis3}
-			\caption{Learning the chocolate bar machine with L* (top to bottom, left to right).\label{fig:lstar-run}}
-		\end{figure}
-
 	\item
-		States are uniquely identified by the amount injected in the machine.
-		The machine does not accept more than 40ct, and the granularity is 5ct.
-		Hence, there are $\frac{40}{5}+1=9$ states.
-		The learned model also contains states, therefore they must be equivalent.
+		States are in principle uniquely identified by the amount injected in the machine.
+		The machine does not accept more than 45ct, and the granularity is 5ct.
+		Hence, there are $\frac{45}{5}+1=10$ states.
+		However, there are two states in which we have 35ct, namely one where we can still insert money
+			(accessed through \enquote{10ct 10ct 5ct 10ct})
+			and one where we cannot (e.g. \enquote{10ct 10ct 10ct 5ct}).
+		Hence, the complete model has 11 states.
+
+		The learned model also contains 11 states, therefore they must be equivalent.
 
 	\item
 		A counter-example $\pi$ consists of a prefix, an input where an inconsistency appears and a suffix showing the inconsistency:
@@ -77,8 +77,34 @@
 	\item
 
 	\item
+		The method with user queries worked very efficiently in combination with L*.
+		It allows the user to insert cleverly chosen counter-examples,
+			but does not ask him as often as other learning methods would do.
+		However, we realise that for more complex systems it may be difficult for the user to provide counter-examples.
+
+		As for the testing method,
+			on our small example a random walk appears to be the fasted.
+		However, as noted in the source code (\texttt{BasicLearner.java}),
+			it may perform worse than the others on large models.
+
 \end{enumerate}
 
+\begin{figure}[p]
+	\includegraphics[width=.5\textwidth]{LStar_hypothesis0}
+	\includegraphics[width=.5\textwidth]{LStar_hypothesis1}
+	\includegraphics[width=.5\textwidth]{LStar_hypothesis2}
+	\includegraphics[width=.5\textwidth]{LStar_hypothesis3}
+	\includegraphics[width=.5\textwidth]{LStar_hypothesis4}
+	\includegraphics[width=.5\textwidth]{LStar_hypothesis5}
+	\caption{Learning the chocolate bar machine with L* (top to bottom, left to right).\label{fig:lstar-run}}
+\end{figure}
+\begin{figure}[p]
+	\ContinuedFloat
+	\includegraphics[width=.5\textwidth]{LStar_hypothesis6}
+	\caption[]{Learning the chocolate bar machine with L* (top to bottom, left to right).\label{fig:lstar-run}}
+\end{figure}
+\thispagestyle{empty}
+
 \section{Bounded Retransmission Protocol}
 
 \end{document}
-- 
cgit v1.2.3

