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+\documentclass{article}
+\usepackage{charter}
+\usepackage{hyperref}
+\usepackage{amssymb}
+\usepackage{amsmath}
+\usepackage{tikz}
+\usetikzlibrary{automata}
+
+\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
+
+\begin{document}
+
+\section*{Homework 6}
+
+\begin{enumerate}
+\item (i) Give the regular expressions for lexing a language
+consisting of whitespaces, identifiers (some letters followed by digits), numbers,
+operations \texttt{=}, \texttt{<} and \texttt{>}, and the keywords
+\texttt{if}, \texttt{then} and \texttt{else}.
+(ii) Decide whether the following strings 
+can be lexed in this language?
+
+\begin{enumerate}
+\item \texttt{"if y4 = 3 then 1 else 3"}
+\item \texttt{"if33 ifif then then23 else else 32"}
+\item \texttt{"if x4x < 33 then 1 else 3"}
+\end{enumerate}
+
+In case they can, give the corresponding token sequences. (Hint: 
+Observe the maximal munch rule and priorities of your regular
+expressions that make the process of lexing unambiguous.)
+
+\item Suppose the grammar
+
+\begin{center}
+\begin{tabular}{lcl}
+$E$ & $\rightarrow$ &  $F \;|\; F \cdot * \cdot F \;|\; F \cdot \backslash \cdot F$\\
+$F$ & $\rightarrow$ & $T \;|\; T \cdot \texttt{+} \cdot T \;|\; T \cdot \texttt{-} \cdot T$\\
+$T$ & $\rightarrow$ & $num \;|\; \texttt{(} \cdot E \cdot \texttt{)}$\\
+\end{tabular}
+\end{center}
+
+where $E$, $F$ and $T$ are non-terminals, $E$ is the starting symbol of the grammar, and $num$ stands for
+a number token. Give a parse tree for the string \texttt{(3+3)+(2*3)}.
+
+\item Define what it means for a grammar to be ambiguous. Give an example of
+an ambiguous grammar.
+
+\item Suppose boolean expressions are built up from
+
+\begin{center}
+\begin{tabular}{ll}
+1.) & tokens for \texttt{true} and \texttt{false},\\
+2.) & the infix operations \texttt{$\wedge$} and \texttt{$\vee$},\\
+3.) & the prefix operation $\neg$, and\\
+4.) & can be enclosed in parentheses.
+\end{tabular}
+\end{center}
+
+(i) Give a grammar that can recognise such boolean expressions
+and (ii) give a sample string involving all rules given in 1.-4.~that 
+can be parsed by this grammar.
+
+
+\end{enumerate}
+
+\end{document}
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: t
+%%% End: