Revisions to L23. just started version of L24.

Lectures/L23_FiniteStateMachines/FiniteStateMachines.tex

@@ -400,6 +400,26 @@ $\mathbf{c}$ & - & - & - & $q_0$\\
 \begin{frame}
 \frametitle{When to use FSMs for Specification?}
 
+\bi
+\item \structure{When is an FSM a good choice for specification?}
+\item \structure{What are some examples of things we would specify using an FSM?}
+\ei
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{When to Potentially use FSMs}
+
+\bi
+\item Describing control flow
+\item Clear finite set of states (or modes)
+\item Specify acceptable strings for a parser
+\item Specifying hardware design
+\item For synchronous models (at any time a global state must be defined and a
+  single transition must occur)
+\ei
 
 \end{frame}
 
@@ -481,7 +501,7 @@ to be $k_1 + k_2 + ... + k_n$)
 
 \begin{itemize}
 \item Events can be viewed as ``pulses'' in time - they do not last (retain their values)
-\item Conditions may retain their values idefinitely
+\item Conditions may retain their values indefinitely
 \end{itemize}
 
 \end{frame}

Lectures/L24_GenericsAndInterfacesInJava/GenericsAndInterfacesInJava.tex

+%\documentclass[t,12pt,numbers,fleqn,handout]{beamer}
+\documentclass[t,12pt,numbers,fleqn]{beamer}
+
+\usepackage{pgfpages} 
+\usepackage{hyperref}
+\hypersetup{colorlinks=true,
+    linkcolor=blue,
+    citecolor=blue,
+    filecolor=blue,
+    urlcolor=blue,
+    unicode=false}
+\urlstyle{same}
+
+\usepackage{booktabs}
+\usepackage{multirow}
+
+\useoutertheme{split} %so the footline can be seen, without needing pgfpages
+
+% \pgfpagesuselayout{resize to}[letterpaper,border
+% shrink=5mm,landscape] %if this is uncommented, the hyperref links do not work
+
+\mode<presentation>{}
+
+\input{../def-beamer}
+
+\newcommand{\topic}{24 Generics and Interfaces in Java}
+
+\input{../titlepage}
+
+\begin{document}
+
+\input{../footline}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Finite State Machines}
+
+\begin{itemize}
+\item Administrative details
+\item Classification of specification styles
+\item Continuation on specification qualities
+\item Homework exercise
+\item How to verify a specification
+\item Finite state machines
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Administrative Details}
+
+\begin{itemize}
+
+\item Some of today's slides adapted from Dr.\ Wassyng's slides (and Ghezzi et al)
+\item A3 deadlines
+\begin{itemize}
+\item Part 1 - Specification: due 11:59 pm Mar 8
+\item Part 2 - Code: due 11:59 pm Mar 20
+\end{itemize}
+
+\item A4
+\bi
+\item Your own design and specification
+\item Due April 3 at 11:59 pm
+\ei
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Same Symbol/Term Different Meaning}
+
+\begin{itemize}
+
+\item \structure{Can you think of some symbols/terms that have different
+    meanings depending on the context?}
+\item \href{http://writingexplained.org/homonyms-and-homophones}{Homonyms}
+\bi
+\item Homograph - same spelling different meaning, maybe different pronunciation
+  (ex.\ bank, bow, biweekly, ...) 
+\item Homophone - same pronunciation, but different meaning, origin or spelling
+  (ex.\ new/knew, to/too/two, ...)
+\ei
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Consistent}
+
+\begin{itemize}
+
+\item Language and terminology must be consistent within the specification
+\item Potential problem with homonyms, for instance consider the symbol $\sigma$
+\begin{itemize}
+\item Represents standard deviation
+\item Represents stress
+\item Represents the Stefan-Boltzmann constant (for radiative heat transfer)
+\end{itemize}
+\item Changing the symbol may be necessary for consistency, but it could adversely effect understandability
+\item Potential problem with \href{https://en.wikipedia.org/wiki/Synonym}{synonyms}
+\begin{itemize}
+\item Externally funded graduate students, versus eligible graduate students, versus non-VISA students
+%ask who would think about graduate school?
+%\item Material behaviour model versus constitutive equation
+\item Enter key versus Return key
+\item \structure{Other examples?}
+\end{itemize}
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Complete}
+
+\begin{itemize}
+
+\item Internal completeness
+\begin{itemize}
+\item The specification must define any new concept or terminology that it uses
+\begin{itemize}
+\item A glossary is helpful for this purpose
+\end{itemize}
+\end{itemize}
+\item External completeness
+\begin{itemize}
+\item The specification must document all the needed requirements
+\begin{itemize}
+\item Difficulty: when should one stop?
+\end{itemize}
+\end{itemize}
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Incremental}
+
+\begin{itemize}
+
+\item Referring to the specification process
+\begin{itemize}
+\item Start from a sketchy document and progressively add details
+\item A document template can help with this
+\end{itemize}
+\item Referring to the specification document
+\begin{itemize}
+\item Document is structured and can be understood in increments
+\item Again a document template can help with this
+\end{itemize}
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Another Example}
+
+\begin{itemize}
+
+\item Operational specification
+\begin{itemize}
+\item ``Let $a$ be an array of $n$ elements. The result of its sorting is an array $b$ of $n$ elements such that the
+first element of $b$ is the minimum of $a$ (if several elements of a have the same value, any one of them is acceptable);
+the second element of $b$ is the minimum of the array of $n-1$ elements obtained from $a$ by removing its minimum
+element; and so on until all $n$ elements of $a$ have been removed.''
+\end{itemize}
+\item Descriptive specification
+\begin{itemize}
+\item ``The result of sorting array $a$ is an array $b$ which is a permutation of $a$ and is sorted.''
+\item \structure<1>{How can we further specify (formalize) the notion of sorted?}
+\item <2-> \structure<2>{$\mbox{sorted}(A) \equiv \forall ( i : \mathbb{N} | 0 \leq i \leq (|A| - 2) : A[i] \leq
+A[i+1])$}
+\end{itemize}
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Classification of Specification Styles}
+
+\begin{itemize}
+
+\item Informal, semi-formal, formal
+\item Operational
+\begin{itemize}
+\item Behaviour specification in terms of some abstract machine
+\end{itemize}
+\item Descriptive
+\begin{itemize}
+\item Behaviour described in terms of properties
+\end{itemize}
+\item The module state machine specification that we use is a mix of operational
+  and descriptive specification - \structure{Why?}
+
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Example Operational Specification}
+
+\begin{itemize}
+
+\item Specification of a geometric figure $E$
+\item $E$ can be drawn as follows
+\begin{enumerate}
+\item Select two points $P_1$ and $P_2$ on a plane
+\item Get a string of a certain length and fix its ends to $P_1$ and $P_2$
+\item Position a pencil as shown in the next figure
+\item Move the pen clockwise, keeping the string tightly stretched,  until you reach the point where you started
+drawing
+\end{enumerate}
+\end{itemize}
+\begin{figure}
+\includegraphics[scale=0.35]{../Figures/DrawingACircle.png}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Example Descriptive Specification}
+
+Geometric figure $E$ is described by the following equation
+$$ a x^2 + b y^2 + c = 0 $$
+where $a$, $b$ and $c$ are suitable constants
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Homework Exercise}
+
+\begin{itemize}
+
+\item Consider the \textbf{line formatter} specification and
+\be
+\item How well does the specification do with respect to the following
+  qualities: abstract, correct, unambiguous, complete, consistent and verifiable?
+\item For a requirement specification like that given, what are the advantages
+  and disadvantages of maintaining both a formal specification and a natural
+  language specification?
+\ee
+\item Even spending 5 minutes thinking about will help when we discuss next week
+\item In repo
+\bi
+\item The
+  \href{https://gitlab.cas.mcmaster.ca/smiths/se2aa4_cs2me3/tree/master/Lectures/LineFormatter}{line
+    formatter specification}
+\item
+  \href{https://gitlab.cas.mcmaster.ca/smiths/se2aa4_cs2me3/blob/master/ReferenceMaterial/Meyer1985.pdf}{Meyer
+    (1985)} ``On Formalism in Specification''
+\ei
+\item Will discuss next day
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{How to Verify a Specification}
+
+\begin{itemize}
+
+\item \structure{Observe} dynamic behaviour of the specified system
+\begin{itemize}
+\item Simulation
+\item Prototyping
+\item ``testing'' the specification
+\end{itemize}
+\item Analyze properties of the specified system
+\item Analogy with traditional engineering
+\begin{itemize}
+\item Physical model of a bridge (prototype)
+\item Mathematical model of a bridge
+\end{itemize}
+\item We will return to this topic when we cover verification (Chapter 6)
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Finite State Machines (FSMs)}
+
+\begin{itemize}
+
+\item Can specify control flow aspects
+\item Defined as
+\begin{itemize}
+\item A finite set of states $Q$
+\item A finite set of inputs $I$
+\item A transition function $\delta: Q \times I \rightarrow Q$ ($\delta$ can be a partial function)
+\end{itemize}
+
+\end{itemize}
+
+\begin{figure}
+\includegraphics[scale=0.25]{../Figures/StateTransitionDiagram.png}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{FSMs Continued}
+
+~\newline
+\begin{tabular}{| c | c | c| c| c|}
+\hline
+~ & $\mathbf{q_0}$ & $\mathbf{q_1}$ &  $\mathbf{q_2}$ & $\mathbf{q_3}$\\
+\hline
+$\mathbf{a}$ & $q_1$ & $q_2$ & - & -\\
+\hline
+$\mathbf{b}$ & - & $q_3$ & $q_3$ & - \\
+\hline
+$\mathbf{c}$ & - & - & - & $q_0$\\
+\hline
+\end{tabular}
+
+\begin{figure}
+\includegraphics[scale=0.25]{../Figures/StateTransitionDiagram.png}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Example: A Lamp}
+
+\bi
+\item \structure{What are the states $Q$ for a typical lamp?}
+\item \structure{What are the set of inputs $I$}
+\item \structure{What is the transition function $\delta$?}
+\ei
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Example: A Lamp}
+
+\begin{figure}
+\includegraphics[scale=0.45]{../Figures/ExampleLamp.png}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Example: A Plant Control System}
+
+\begin{figure}
+\includegraphics[scale=0.45]{../Figures/PlantControlSystem.png}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{A Refinement}
+
+\begin{figure}
+\includegraphics[scale=0.45]{../Figures/ARefinement.png}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{When to use FSMs for Specification?}
+
+\bi
+\item \structure{When is an FSM a good choice for specification?}
+\item \structure{What are some examples of things we would specify using an FSM?}
+\ei
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{When to Potentially use FSMs}
+
+\bi
+\item Describing control flow
+\item Clear finite set of states (or modes)
+\item Specify acceptable strings for a parser
+\item Specifying hardware design
+\item For synchronous models (at any time a global state must be defined and a
+  single transition must occur)
+\ei
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Classes of FSMs}
+
+\begin{itemize}
+\item Deterministic/nondeterministic
+\item FSMs as recognizers - introduce final states
+\item FSMs as transducers - introduce set of output
+\item ...
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{FSMs as Recognizers}
+
+\begin{figure}
+\includegraphics[scale=0.5]{../Figures/FSM_as_Recognizers.png}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{FSMs as Recognizers Continued}
+
+\begin{figure}
+\includegraphics[scale=0.5]{../Figures/FSM_as_Recognizers2.png}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Limitations}
+
+\begin{itemize}
+\item Finite memory
+\item State explosion - Given a number of FSMs with $k_1, k_2, ... k_m$ states, their composition is an FSM with $k1 
+\times k_2 \times ... \times k_n$.  This growth is exponential with the number of FSMs, not linear (we would like it 
+to be $k_1 + k_2 + ... + k_n$)
+\end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{State Explosion: An Example}
+
+\begin{figure}
+\includegraphics[scale=0.5]{../Figures/StateExplosionExample.png}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{The Resulting FSM}
+
+\begin{figure}
+\includegraphics[scale=0.5]{../Figures/StateExplosionResult.png}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Events Versus Conditions}
+
+\begin{itemize}
+\item Events can be viewed as ``pulses'' in time - they do not last (retain their values)
+\item Conditions may retain their values idefinitely
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{FSM Example: Security Alarm}
+
+\begin{figure}
+\includegraphics[scale=0.45]{../Figures/Security.pdf}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Security Alarm Example Continued}
+
+\begin{figure}
+\includegraphics[scale=0.6]{../Figures/States_ass4.pdf}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\end{document}
\ No newline at end of file