feat(dissertation): write formal methods background in full

pub/dissertation/chapters/background.tex

@@ -168,21 +168,34 @@ situations where the crew may completely ignore safety procedures and systems.
 % TODO add quick overview of what Formal Methods are
 % Potential resource: https://shemesh.larc.nasa.gov/fm/fm-what.html
 
-\begin{itemize}
-  \item Formal methods is a mathematical technique that can be used towards the
-    verification of a system~\cite{nasa:formal}
-  \item This can be used to verify correctness of all the inputs in a system~\cite{nasa:formal}
-  \item Hence, as dealing with safety, it would be beneficial to have
-    the logic of this testing tool verified, to avoid bugs and misleading results
-  \item Airbus also uses formal methods in their avionics systems validation and
-    verification process~\cite{airbus:formal}
-  \item Some examples where Airbus used formal methods was during the development
-    for the Airbus A380, where they used it for proof of absence of stack overflows
-    and analysis of the numerical precision and stability of floating-point operators
-    to name a few~\cite{airbus:formal}
-  \item There are a multitude of specification languages, each of them
-    having their own reasons % TODO don't know if this should be included
-\end{itemize}
+% \begin{itemize}
+%   \item Formal methods is a mathematical technique that can be used towards the
+%     verification of a system~\cite{nasa:formal}
+%   \item This can be used to verify correctness of all the inputs in a system~\cite{nasa:formal}
+%   \item Hence, as dealing with safety, it would be beneficial to have
+%     the logic of this testing tool verified, to avoid bugs and misleading results
+%   \item Airbus also uses formal methods in their avionics systems validation and
+%     verification process~\cite{airbus:formal}
+%   \item Some examples where Airbus used formal methods was during the development
+%     for the Airbus A380, where they used it for proof of absence of stack overflows
+%     and analysis of the numerical precision and stability of floating-point operators
+%     to name a few~\cite{airbus:formal}
+%   \item There are a multitude of specification languages, each of them
+%     having their own reasons % TODO don't know if this should be included
+% \end{itemize}
+
+Formal methods is a mathematical technique that can be used towards the verification
+of a system, that could either be a piece of software or hardware.
+Therefore, this can be used to verify correctness of all the inputs in a system.~\cite{nasa:formal}
+Hence, as this project is dealing with safety, it would be beneficial to use
+formal methods for testing and verification.
+
+An example of where formal methods is used within aviation is by Airbus, where
+it was used during the development of the Airbus A380. Formal methods was used to test
+the A380 for proof of absence of stack overflows and analysis of the numerical precision
+and stability of floating-point operators to name a few.~\cite{airbus:formal}
+
+% TODO maybe add a section about the amount of specification languages that exist?
 
 
 %%%%% SOLUTION STACK %%%%%