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\vspace*{\fill}
\begin{center}

{\huge Data Diversity: A Search For Direction}

\vspace{1in}

{\huge Frederick C. Harris, Jr.}
\end{center}
\vspace*{\fill}

\newpage
\huge
\baselineskip=40pt
\begin{description}
\item Introduction
	\begin{enumerate}
	\item The Problem

	\item Current ways to solve it
		\begin{enumerate}
		\item $N$-version Programming
		\item Recovery Blocks
		\end{enumerate}

	\item Ammann and Knight 
		\begin{enumerate}
		\item Design Diversity
		\item Data Diversity
		\end{enumerate}
	\item This Research

	\end{enumerate}
		\normalsize
		\begin{figure}[h]
			\centering
			\input{figure/pic.tex}
			\caption{\label{fig:model}System Model}
		\end{figure}
		\huge
\newpage
\baselineskip=40pt
\item A Sample Module
	\begin{enumerate}
	\item The Programmers
		\begin{itemize}
		\item Seminar participants -- Fall 1989
		\end{itemize}
	\item The Specifications
		\begin{itemize}
		\item NASA Planetary Lander
		\end{itemize}
	\item The Acclerometer Sensor Processing Module

	Transform the accelerometer data (A\_COUNTER) into
	vehicle accelerations (A\_ACCELERATION).

\newpage
\Large
\baselineskip=30pt
		\begin{enumerate}
		\item A\_GAIN := A\_GAIN\_0 \newline 
		+ (G1 * ATMOSPHERIC\_TEMP) \newline
		+ (G2 * $\makebox{ATMOSPHERIC\_TEMP}^{2}$)
		\item A\_ACCELERATION\_M := A\_BIAS \newline
		+ A\_GAIN * A\_COUNTER
		\item Shift A\_STATUS and A\_ACCELERATION right by 1 column.
		\item A\_ACCELERATION := ALPHA\_MATRIX \newline
		* A\_ACCELERATION\_M
		\item For each row of A\_STATUS and A\_ACCELERATION: 
		\begin{itemize}
		\item If any of the previous three values of A\_STATUS is 
		{\it unhealthy}, set A\_STATUS(i,0) to {\it healthy}.  
		\item Otherwise, for each of the three dimensions in \newline
		A\_ACCELERATION calculate the mean ($\mu$) \newline
		and the standard deviation ($\sigma$).  
			\begin{itemize}
			\item If $|\mu$ - A\_ACCELERATION(i,0)$| > $ 
			A\_SCALE*$\sigma$, then \newline
			set A\_ACCELERATION(i,0) to $\mu$ and \newline
			set A\_STATUS(i,0) to {\it unhealthy}.
			\end{itemize}
		\end{itemize}
		\end{enumerate}  

	\huge
	\baselineskip=40pt
	\vspace*{\fill}
	\end{enumerate}


\newpage
\item Mutation Analysis
	\begin{enumerate}
	\item Vocabulary Terms
		\begin{enumerate}
		\item Mutant Operators
		\item How to kill a mutant
		\item Equivalent mutants
		\end{enumerate}
	\item Mothra
		\begin{enumerate}
		\item History
		\item Constraints
		\item Godzilla
		\end{enumerate}
	\item What happened to ASP
		\begin{enumerate}
		\item 3778 non-equivalent mutants
		\item 30 test cases
			\begin{itemize}
			\item One was troublesome (4 out of 5 failed)
			\item This was the starting point \newline for the Pilot Study
			\end{itemize}
		\end{enumerate}
	\end{enumerate}
\newpage
	\vspace*{2.0in}
	\begin{tabular}{ll}
	 	& FUNCTION MAX(M,N) \\
	1	& MAX = M \\
	\#	& MAX = N \\
	\#	& MAX = ABS(N) \\
	2	& IF (N .GT. M) MAX = N \\
	\#	& IF (N .LT. M) MAX = N \\
	\#	& IF (N .GE. M) MAX = N \\
	3	& RETURN
	\end{tabular}

\newpage
\item Surface Construction
	\begin{enumerate}
	\item ASP has too many inputs for a Pilot Study
	\item Fixed all input variables except G1 and G2.
	\item Constructed a surface, M,  of Mutant Kill Scores 
	from a uniform sampling of G1 and G2 inputs.
	\item M(G1,G2) ranged from 1924 - 2092
	\end{enumerate}
	\vspace*{\fill}
	\begin{figure}[hb]
		\centering
		\vspace{4.5in}
		% now load in the PostScript image
		% 2.5 6.0 translations
		\special{psfile=surface/floyd2b.ps}
		\caption{\label{fig:surface} Digitized image of G1 and G2 surface}
	\end{figure}

\newpage

\item Retry Block
	\begin{enumerate}
	\item Definition: 
		\begin{enumerate}
		\item Execute the N-versions
		\item If there is a majority we are done
		\item Else ``tweak'' the input data and re-execute all versions
		of the code
		\end{enumerate}
	\item This was Gradient Based
		\begin{enumerate}
		\item What is a gradient?
		\item How did I find it?
		\end{enumerate}
	\item Four Blocks were constructed
		\begin{enumerate}
		\item Random (Ammann and Knight)
		\item Up
		\item Down
		\item Level
		\end{enumerate}
	\end{enumerate}

\newpage
\item Results
	\begin{enumerate}
	\item Find Some failures to retry
		\begin{itemize}
		\item Generate a random case from (G1,G2)
		\item Check for system failure
		\item Collect 15,000 of these failure points
		\item On the average there were 62 successes for every failure
		\end{itemize}

		\normalsize
		\begin{figure}[ht]
		\centering
		%\input{failure.plot/failure.tex} 
		\input{failure.plot/failure2.tex} % just has box outline w/o data
		\caption{\label{fig:failures}Failure points in (G1,G2) space.}
		\end{figure}
		\huge
		\baselineskip=40pt

\newpage

	\item What were the results of the retry blocks?

		\begin{itemize}
		\item This was dependent upon direction \newline and distance

		\vspace*{0.75in}
		\normalsize
		\begin{figure}[h]
		\centering
		\input{retry.plot2/retry-sl.tex}
		%\input{retry.plot/retry2.tex} % just has box outline w/o data
		\caption{\label{fig:retry}Failures surviving retry.}
		\end{figure}
		\vspace*{0.5in}
		\huge
		\baselineskip=40pt

		\item Random Direction has a 90\% success rate
		\end{itemize}
\newpage
	\setcounter{enumi}{1}

	\item What were the results of the retry blocks?

		\begin{itemize}
		\item This was dependent upon direction \newline and distance
		\vspace*{\fill}
		\normalsize
		\begin{figure}[h]
		\centering
		\input{retry.plot2/retry.tex}
		%\input{retry.plot/retry2.tex} % just has box outline w/o data
		\caption{\label{fig:retry}Failures surviving retry.}
		\end{figure}
		\vspace*{\fill}
		\huge
		\baselineskip=40pt

		\item Random Direction has a 90\% success rate
		\item Any of the 3 Gradient-based directions \newline
		 provides better results
		\end{itemize}
	\end{enumerate}


%		\vspace*{1in}

\newpage

\item Future Work
	\begin{enumerate}
	\item Remove the constraints of this pilot study.
		\begin{itemize}
		\item This would require the computationally \newline
		expensive task of constructing a \newline
		Mutation Kill-Score Surface
		\end{itemize}
	\item The effects of multiple retries, \newline
	subject to a real-time constraint, \newline
	should be explored.
	\end{enumerate}

\end{description}
\end{document}
