\documentclass{article}

\usepackage{a4wide}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage[all]{xypic}

\newcommand{\ra}{\rightarrow}
\newcommand{\un}{\text{ \textsf{U} }}
\newcommand{\ev}{\lozenge}
\newcommand{\al}{\square}
\newcommand{\nx}{\bigcirc}

\begin{document}
\begin{enumerate}
	\item
		$\xymatrix{
			\ar[dr]\\
				& *+[o][F-]{s_0}\\
			*+[o][F-]{nc_1} & & *+[o][F-]{nc_1}
		}$
	\item
		$\al(crit_0\veebar crit_1)$
	\item 
		We define:\\
		$\displaystyle AP=\bigcup_{i\in N}\{lift_n, door_n,call_n\},
		N=\{0, 1, 2, 3\}$
		\begin{enumerate}
			\item
				$\forall n\in N\al(door_m\ra lift_n)$
			\item
				$\forall n\in N\al(call_n\ra\ev lift_n)$
			\item
				$\al\ev lift_0$
			\item
				$\al call_3\rightarrow\bigcirc lift_3$
		\end{enumerate}
	\item\strut\\
		$\begin{array}{ll}
			\varphi_1=\ev\al c & 
				s_2\ra s_4\overline{\ra s_5}\\
			\varphi_2=\al\ev c &
				s_2\ra s_4\overline{\ra s_5}\\
			\varphi_3=\nx\neg c\rightarrow\nx\nx c &
				s_2\ra s_4\overline{\ra s_5}\\
			\varphi_4=\al a & 
				\text{Impossible. $a$ only holds in $s_1$ and in $s_5$.}\\
			& \text{$s_1$ we can only leave through a state where $\neg a$}\\
			& \text{$s_5$ we can not reach through $s_1$ without passing
				through a $\neg a$ state}\\
			\varphi_5=a\un\al(b\vee c) &
				s_1\ra s_4\overline{\ra s_5}\\
			\varphi_6=(\nx\nx b)\un(b\vee c) &
				s_2\ra s_4\overline{\ra s_5}
		\end{array}$
\end{enumerate}
\end{document}
