%% LyX 1.1 created this file.  For more info, see http://www.lyx.org/.
%% Do not edit unless you really know what you are doing.
\documentclass[12pt,oneside,english,english,english]{amsart}
\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage{babel}
\usepackage{amssymb}
\usepackage[dvips]{color}
\makeatletter

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
\providecommand{\LyX}{L\kern-.1667em\lower.25em\hbox{Y}\kern-.125emX\@}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
 \theoremstyle{plain}    
 \newtheorem{thm}{Theorem}[section]
 \numberwithin{equation}{section} %% Comment out for sequentially-numbered
 \numberwithin{figure}{section} %% Comment out for sequentially-numbered
 \theoremstyle{plain}    
 \newtheorem{cor}[thm]{Corollary} %%Delete [thm] to re-start numbering
 \newtheorem{prop}[thm]{Proposition} %%Delete [thm] to re-start numbering
 \theoremstyle{definition}
 \newtheorem{defn}[thm]{Definition}
 \theoremstyle{definition}
 \newtheorem{example}[thm]{Example}
\newcommand{\field}[1]{\mathbb{#1}}
\newcommand{\R}{\field{R}}
\newcommand{\Z}{\field{Z}}
\newcommand{\Q}{\field{Q}}
 \newcommand{\lyxaddress}[1]{
   \par {{\bf R}aggedright #1 
   \vspace{1.4em}
   \noindent\par}
 }


\begin{document}

\begin{center}
{\Large{\color{red}Homework 1 (DFA and NFA)}}

{\it Due Friday, Feb 16, 07, at 3:00 PM in Class}
\end{center}

\begin{enumerate}

\item Construct a DFA that accepts 
\[
L = \{ x \in \{0,1\}^* ~|~ |x| \text{ is a multiple of 3}\}.
\]
\item Construct a DFA that accepts 
\[
L = \{ x \in \{0,1\}^* ~|~ |x| \leq 3\}.
\]
\item Construct an NFA that accepts
\[
L = \{ x \in \{0,1\}^* ~|~x\text{ contains an even number of zeros or exactly two 1's}\}.
\]
\end{enumerate}

{\bf Note:} Next homework is on NFA, equivalence of NFA and DFA, and regular languages.

\end{document}
