1 \documentclass{article}

     2 \usepackage{charter}

     3 \usepackage{hyperref}

     4 \usepackage{amssymb}

     5 \usepackage{proof}

     6 

     7 \begin{document}

     8 

     9 \section*{Homework 7}

    10 

    11 \begin{enumerate}

    12 \item Suppose a judgement is of the form:

    13 \begin{center}

    14 $Alice\;\textit{says}\;S \wedge Bob\;\textit{says}\;S \vdash Bob\;\textit{says}\;S \wedge Alice\;\textit{says}\;S$

    15 \end{center}

    16 

    17 Assume you want to use the inference rule

    18 

    19 \begin{center}

    20 \mbox{\infer{\Gamma \vdash F_1 \wedge F_2}{\Gamma \vdash F_1 & \Gamma \vdash F_2}}

    21 \end{center}

    22 

    23 for constructing a proof of the judgement. What do the premises look like? 

    24 

    25 \item The informal meaning of the formula \mbox{$P\;\mapsto\;Q$} is `$P$ speaks for

    26 $Q$'. Give a definition for this formula in terms of $\textit{says}$.

    27 

    28 \item In Unix, what should be the general architecture of a network application that 

    29 processes potentially hostile data from the Internet? (Hint: Focus on the fact that in Unix

    30 you can give different privileges to processes.)

    31 

    32 \item Explain what are the differences between dictionary and brute forcing attacks  against  passwords.

    33 

    34 \end{enumerate}

    35 \end{document}

    36 

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