e1-4 done

diff --git a/.gitignore b/.gitignore
new file mode 100644 (file)
index 0000000..8164e02
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,3 @@
+*.log
+*.aux
+*.pdf

diff --git a/Makefile b/Makefile
new file mode 100644 (file)
index 0000000..2915da3
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,16 @@
+LATEX:=pdflatex
+DOCUMENTS:=e1.pdf
+
+.PHONY: all clean clobber
+
+all: $(DOCUMENTS)
+
+%.pdf: %.tex
+       $(LATEX) $(basename $<)
+       $(LATEX) $(basename $<)
+
+clobber:
+       $(RM) -v *.pdf
+
+clean:
+       $(RM) -v *.aux *.log

diff --git a/e1.tex b/e1.tex
new file mode 100644 (file)
index 0000000..6155f3b
--- /dev/null
+++ b/e1.tex
@@ -0,0 +1,37 @@
+\documentclass{article}
+
+\usepackage{a4wide}
+\usepackage{amssymb}
+\usepackage{amsmath}
+
+\newcommand{\ra}{\rightarrow}
+\newcommand{\un}{\text{ \textsf{U} }}
+\newcommand{\ev}{\lozenge}
+\newcommand{\al}{\square}
+\newcommand{\nx}{\bigcirc}
+
+\begin{document}
+\begin{enumerate}
+       \item
+       \item
+       \item
+       \item\strut\\
+               $\begin{array}{ll}
+                       \phi_1=\ev\al c & 
+                               s_2\ra s_4\overline{\ra s_5}\\
+                       \phi_2=\al\ev c &
+                               s_2\ra s_4\overline{\ra s_5}\\
+                       \phi_3=\nx\neg c\rightarrow\nx\nx c &
+                               s_2\ra s_4\overline{\ra s_5}\\
+                       \phi_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}\\
+                       \phi_5=a\un\al(b\vee c) &
+                               s_1\ra s_4\overline{\ra s_5}\\
+                       \phi_6=(\nx\nx b)\un(b\vee c) &
+                               s_2\ra s_4\overline{\ra s_5}
+               \end{array}$
+\end{enumerate}
+\end{document}