update spellcheck

[ar1516.git] / a2 / 1.tex

diff --git a/a2/1.tex b/a2/1.tex
index 8aeb788..324e7d8 100644 (file)
--- a/a2/1.tex
+++ b/a2/1.tex
@@ -41,7 +41,7 @@ formula called $trans$. We introduce a function $conn(s)$ that returns the set
 of all cities connected to city $s$. $(2)$ deals with the fact that the truck
 can not dump any food in city $S$ and constraints the amount of food dumped in
 the city. $(3)$ deals with the fact that the dumped food is added to the
-current stock of the city. Subformula $(4)$ deals with the fact that if the
+current stock of the city. Sub formula $(4)$ deals with the fact that if the
 truck is in $S$ it is replenished and otherwise the dumped load is subtracted
 from the trucks load. Finally $(5)$ deals with the other cities which will have
 their stock decremented with the distance traveled.
@@ -61,7 +61,7 @@ We tie all this together in one big formula that is as follows:
 $$const\wedge initial\wedge
 \bigwedge_{i\in I}\left(constraints\wedge trans\right)$$
 
-\begin{enumerate}[a.]
+\begin{enumerate}[(a)]
        \item \emph{Show that it is impossible to deliver food packages in such a
                way that each of the villages consumes one food package per time unit
                forever.}
@@ -69,7 +69,7 @@ $$const\wedge initial\wedge
                state where a city is without food. Therefore we try to find proof that
                the truck is actually capable of keeping all cities saturated.
 
-               To show this we need to prove that there is a state in the statespace
+               To show this we need to prove that there is a state in the state space
                that is exactly the same as some previous state. To do this we add the
                following formula to the conjunction.
                $$\bigvee_{i\in I}\bigvee_{j\in \{0\ldots i-1\}}\left(
@@ -107,10 +107,10 @@ $$const\wedge initial\wedge
                infinite path starting in a node $v$ if and only if there is a path
                from $v$ to a node $w$ for which there is a non-empty path from $w$ to
                itself.)}
-               Solution idem to $a.$. Just imagine the truck operator glueing $20$
+               Solution idem to $(a)$. Just imagine the truck operator glueing $20$
                food packages to the truck which he can not deliver.
        \item \emph{Figure out whether it is possible if the capacity of the truck
                is set to $318$.}
-               Solution idem to $a.$. Just imagine the truck operator glueing $18$
+               Solution idem to $(a)$. Just imagine the truck operator glueing $18$
                food packages to the truck which he can not deliver.
 \end{enumerate}