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diff --git a/assignment1.tex b/assignment1.tex new file mode 100644 index 0000000..7693073 --- /dev/null +++ b/assignment1.tex @@ -0,0 +1,42 @@ +\documentclass[10pt,a4paper]{article} + +\usepackage{geometry} +\usepackage[english]{babel} + +\usepackage{enumitem} +\setenumerate[1]{label=\alph*)} + +\usepackage{fancyhdr} +\renewcommand{\headrulewidth}{0pt} +\renewcommand{\footrulewidth}{0pt} +\fancyhead{} +\fancyfoot[C]{Copyright {\textcopyright} 2016 Camil Staps} +\pagestyle{fancy} + +\usepackage{sv} + +\title{Software Verification - assignment 1} +\author{Camil Staps} + +\begin{document} + +\maketitle +\thispagestyle{fancy} + +\setcounter{section}{2} +\section{Expressing the ABP in LTL} + +\begin{enumerate} + \item $\always(\lnot(A_{S0}\land A_{S1}))$. + \item $\always(A_{S0}\lor A_{S1})$. + \item $\always\eventually(A_{S0}\lor A_{S1})$. + \item $\always(A_{Sb}\then\eventually B_{Sb})$, $b\in\{0,1\}$. + \item $\always(A_{Sb}\then\next B_{Rb})$, $b\in\{0,1\}$. + \item $\always(B_{R0}\then B_{S0}\until B_{R1})$. + \item $\always(A_{S0}\then \lnot A_{S1}\until A_{R0})$. + \item Cannot be expressed: there are no atomic propositions defined for `$A$ can send'. + \item $\always(A_{Sb}\then(\eventually B_{Rb})\lor(\always\lnot B_{Rb}))$, $b\in\{0,1\}$. However, this is rather silly, since $\always((\eventually p)\lor(\always\lnot p))$ always holds. +\end{enumerate} + +\end{document} + |