
diff -r ffde837b1db1 -r 397ecdafefd8 handouts/ho01.tex
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+\documentclass{article}
+\usepackage{charter}
+\usepackage{hyperref}
+\usepackage{amssymb}
+\usepackage{amsmath}
+\usepackage[T1]{fontenc}
+
+\begin{document}
+
+\section*{Handout 1}
+
+This course is about processing of strings. Lets start with what we mean by \emph{string}. Strings
+are lists of characters drawn from an \emph{alphabet}. If nothing else is specified, we usually assume 
+the alphabet are letters $a$, $b$, \ldots, $z$ and $A$, $B$, \ldots $Z$. Sometimes we explicitly
+restrict strings to only contain the letters $a$ and $b$. Then we say the alphabet is the set $\{a, b\}$.
+
+There are many ways how we write string. Since they are lists of characters we might write
+them as {\it "hello"} being enclosed by double quotes. This is a short-hand for the list
+
+\[
+[\text{\it h, e, l, l, o}]
+\]
+
+\noindent
+The important point is that we can always decompose strings. For example we often consider the
+first character of a string, say $h$, and the ``rest''  of a string {\it "ello"}. 
+There are also some subtleties with the empty string, sometimes written as {\it ""} or as the empty list
+of characters $[\,]$. 
+
+We often need to talk about sets of strings. For example the set of all strings
+
+\[
+\{\text{\it "", "a", "b", "c",\ldots,"z", "aa", "ab", "ac", \ldots, "aaa", \ldots}\}
+\]
+
+\noindent
+Any set of strings, not just the set of all strings, is often called a \emph{language}. The idea behind
+this choice is that if we enumerate, say, all words/strings from a dictionary, like 
+
+\[
+\{\text{\it "the", "of", "milk", "name", "antidisestablishmentarianism", \ldots}\}
+\]
+
+\noindent
+then we have essentially described the English language, or more precisely all
+strings that can be used in a sentence of the English language. French would be a
+different set of string, and so on. In the context of this course, a language might 
+not necessarily make sense from a natural language perspective. For example
+the set of all strings from above is a language, as is the empty set (of strings). The
+empty set of strings is often written as $\varnothing$ or $\{\,\}$. Note that there is a 
+difference between the empty set $\{\,\}$ and the set that contains the empty string $\{\text{""}\}$.
+
+\end{document}
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: t
+%%% End: 




