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\section*{Homework 7}

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\item Suppose a judgement is of the form:
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$Alice\;\textit{says}\;S \wedge Bob\;\textit{says}\;S \vdash Bob\;\textit{says}\;S \wedge Alice\;\textit{says}\;S$
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Assume you want to use the inference rule

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\mbox{\infer{\Gamma \vdash F_1 \wedge F_2}{\Gamma \vdash F_1 & \Gamma \vdash F_2}}
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for constructing a proof of the judgement. What do the premises look like? 

\item The informal meaning of the formula \mbox{$P\;\mapsto\;Q$} is `$P$ speaks for
$Q$'. Give a definition for this formula in terms of $\textit{says}$.

\item In Unix, what should be the general architecture of a network application that 
processes potentially hostile data from the Internet? (Hint: Focus on the fact that in Unix
you can give different privileges to processes.)

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

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