1.1 --- a/doc-src/isac/jrocnik/bakkarbeit_jrocnik.tex Wed Oct 19 23:11:45 2011 +0200
1.2 +++ b/doc-src/isac/jrocnik/bakkarbeit_jrocnik.tex Thu Oct 20 19:41:46 2011 +0200
1.3 @@ -24,6 +24,8 @@
1.4 \usepackage{setspace}
1.5 \usepackage[pdfpagelabels]{hyperref}
1.6 \usepackage{longtable}
1.7 +\usepackage{float} %For restylefloat
1.8 +\restylefloat{table}
1.9
1.10 %isabelle relevant packages
1.11 \usepackage{isabelle,isabellesym}
1.12 @@ -32,7 +34,6 @@
1.13 \def\isac{${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}
1.14 \def\sisac{\footnotesize${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}
1.15
1.16 -
1.17 %----------// BEGIN DOCUMENT \\----------%
1.18
1.19 \begin{document}
1.20 @@ -107,7 +108,7 @@
1.21 The motivation to this thesis mainly takes it source from the feeling of understanding difficult signal processing tasks and the will to help others to get this feeling to.
1.22 \par Signal Processing requieres a huge range of mathematic knowledge as well as a feeling for simplification and number tricks but even though this fact, the operations themself are no higher ones. The main task is to understand. Aside this description we think of the classic math ideas and techniques, consisting of predefined formulas, notations and forumularsations we learn.
1.23 \par Mathematics mechanized in Computer Theorem Provers (\emph{CTP}) has (almost) a problem with traditional mathematical notations (predicate calculus) for axioms, definitions, lemmas, theorems as a computer programm or script is not able to interpret every greek or latin letter and every greek, latin or whatever calculations symbol. Also if we would be able to handle thehse symbols we would have a problem to interpret them correctly. In different problems, symbols and letters have different meanings and ask for different ways to get through. Exclusive from the input, also the output can be a problem. We are familar with a specified notations and style taught in university but a computer programm has no knowledge of the form probved by a professor and the maschines themselve also have not yet the possibilities to print every symbol (correct) Recent developments provide proofs in a humand readable format but according to the fact that there is no mony for good working formel editors yet, the style is one thing we have to live with.
1.24 -\par This thesis tries to \empg{connect} these two worlds and is one of the first guidelines to implement problem classes in {\sisac}. For others see related works. %--01--
1.25 +\par This thesis tries to \emph{connect} these two worlds and is one of the first guidelines to implement problem classes in {\sisac}. For others see related works in section \ref{sec:related}.
1.26 The major challenge of the practical part, of this thesis, is, that "`connecting the two worlds"' involves programming in a CTP-based programming language which is in a very early state of prototyping. There is no concrete experience data ready to grep.
1.27
1.28 \subsection{Mechanization of Mathematics}
1.29 @@ -119,11 +120,19 @@
1.30 \subsection{Goals of the Thesis}
1.31 Imagine a piece of software would be able to support you by understanding every problem class, upcoming in the first years attending university - wouldn't it be great?
1.32 \par {\sisac{}} tries to do that, but the current state of the art is miles away from this goal and a single implementation of a problem is not enough to cahnge this circumstamce. Through this fact it is all the more essential to try, test, research and document the implementation of problem classes from "`real world"' applications. Responding to the abstract at the begin of this document the thesis has two folds; on the one hand certainly to provide interactiv course material for Signal Processing (which means to implement a single problem provided by the Institute of Signal Processing and Speech Communication (SPSC); follow up Calulcations), and to extract experience data respectively help the {\sisac{}}-team by setting up a detailed description of technicalities hacking {\sisac{}} on the other hand.
1.33 +\par Another goal is to demonstrate the power and attractivity of {\sisac}.
1.34
1.35 -\section{Mechanization of Mathematics for SP Problems}
1.36 -
1.37 +\section{Mechanization of Signal Processing Problems}
1.38 \subsection{Relevant Knowledge available in Isabelle}
1.39 -todo
1.40 +Isabelle is developed now for a long time and so we are able to access a huge range of theories and usefull snipsets. The main problem according this snipsets is that isabelle still is a theorem proofer and not an algebra system. But due the work of the {\sisac}-development team there are already also many calculation examples provided.
1.41 +\par The SPSC provided a list of problems which are often done wrong or are missunderstood by studentsin term of the problem classes. Out of these tasks we tried to extract the core operations and looked up which parts are already implemented or usefull. The provided problems are:
1.42 +\begin{itemize}
1.43 +\item Fourier-Transformation
1.44 +\item Convolution
1.45 +\item Inverse z-Transformation and partial fraction decomposition
1.46 +\item Indextransformation
1.47 +\end{itemize}
1.48 +Following the collection and evaluation of core operations collated with isabelle:
1.49
1.50 \paragraph{example FFT}, describe in detail !!!!
1.51
1.52 @@ -140,12 +149,62 @@
1.53
1.54 partial fractions, cancellation of multivariate rational terms, ...
1.55
1.56 -\subsection{Survey: Available Knowledge and Selected Problems}
1.57 -todo
1.58 +\subsection{Survey: Requiered Knowledge and Selected Problem(s)}
1.59 +Following tables are showing the expected development effort for speciefic problems. The values are only very inaccurately approximations of the real work, but needed as a basis for descieding with which problem to start:
1.60
1.61 -estimate gap (@) for each problem (tables)
1.62 +\begin{table}[!H]
1.63 +\begin{centering}
1.64 +\begin{tabular}{p{4cm}|p{5cm}|rp{2.5cm}}
1.65 +requirements & comments &effort\\ \hline\hline
1.66 +solving Intrgrals & simple via propertie table & 20\\
1.67 + & \emph{real} & MT\\ \hline
1.68 +transformation table & simple transform & 20\\ \hline
1.69 +visualisation & backend & 10\\ \hline
1.70 +example collection & with explanations & 20\\ \hline\hline
1.71 +\multicolumn{2}{c|}{} & 70-80\\
1.72 +\end{tabular}
1.73 +\par\end{centering}
1.74 +\caption{Fourier-Transformation development effort}
1.75 +\end{table}
1.76
1.77 -conclusion: following order for implementing the problems ...
1.78 +\begin{table}[H]
1.79 +\begin{centering}
1.80 +\begin{tabular}{p{4cm}|p{5cm}|rp{2.5cm}}
1.81 +requirements & comments &effort\\ \hline\hline
1.82 +simplify rationals & \sisac & 0\\ \hline
1.83 +define $\sum\limits_{i=0}^{n}i$ & partly \sisac & 10\\ \hline
1.84 +simplify sum & termorder & 10\\
1.85 + & simplify rules & 20\\
1.86 + & use simplify rationals& 0\\ \hline
1.87 +index adjustments & with unit step & 10\\ \hline
1.88 +example collection & with explanations & 20\\ \hline\hline
1.89 +\multicolumn{2}{c|}{} & 70-90\\
1.90 +\end{tabular}
1.91 +\par\end{centering}
1.92 +\caption{Convolution Operations development effort}
1.93 +\end{table}
1.94 +
1.95 +\begin{table}[H]
1.96 +\begin{centering}
1.97 +\begin{tabular}{p{4cm}|p{5cm}|rp{2.5cm}}
1.98 +requirements & comments &effort\\ \hline\hline
1.99 +solve for part.fract. & \sisac: degree 2 & 0\\
1.100 + & complex nomminators & 30\\
1.101 + & degree > 2 & MT\\ \hline
1.102 +simplify polynomial & \sisac & 0\\
1.103 +simplify rational & \sisac & 0\\ \hline
1.104 +partial fraction & degree 2, & 20\\
1.105 +decomposition & specification, method& 30\\ \hline
1.106 +${\cal Z}^{-1}$ table & explanations, figures& 20\\ \hline
1.107 +example collection & with explanations & 20\\ \hline\hline
1.108 +\multicolumn{2}{c|}{} & 90-120\\
1.109 +% & & 1 MT
1.110 +\end{tabular}
1.111 +\par\end{centering}
1.112 +\caption{Z-Transformation development effort}
1.113 +\end{table}
1.114 +
1.115 +As conclusion of the summerized efforts it is evident that only one topic can be tried to realized as a baccalaureate thesis. In accord with Dr. Neuper we decided after some practical tests to start with the implementation of the (Inverse) Z-Transformation. The Reason is that this topic can mostly be done with knowledge which was already tried to be mechanized in {\sisac}.
1.116
1.117 \subsection{Formalization of missing knowledge in Isabelle}
1.118 todo
1.119 @@ -215,30 +274,30 @@
1.120 todo
1.121 \section{Bericht zum Projektverlauf}
1.122 todo
1.123 -
1.124 -\section{Related Work and Open Questions}
1.125 -todo
1.126 -
1.127 -See ``introduction'': This thesis tries to connect these two worlds ... this trial is one of the first; others see related work
1.128 -
1.129 \section{Abschliesende Bemerkungen}
1.130 todo
1.131
1.132 +\clearpage
1.133
1.134 +%----------// RELATED \\-----------%
1.135
1.136 +\section{Related Work and Open Questions \label{sec:related}}
1.137 +List of related work
1.138 +See ``introduction'': This thesis tries to connect these two worlds ... this trial is one of the first; others see related work
1.139 \clearpage
1.140
1.141 +%----------// BIB \\-----------%
1.142 +
1.143 \renewcommand{\refname}{\section{Sources}} % Using "Sources" as the title of the section
1.144 \bibliographystyle{alpha}
1.145 \bibliography{references}
1.146 -
1.147 \clearpage
1.148
1.149 -
1.150 %----------// APPENDIX \\-----------%
1.151
1.152 \appendix
1.153
1.154 +%----------// WORK TIME \\-----------%
1.155
1.156 \section{Stundenliste}
1.157 \begin{footnotesize}