When parsed the sokoban screen is stripped of all walls and unreachable empty
spaces are removed.
-Let $T=\{free,box,target,agent,targetagent,targetbox\}$ be the set of
-possible states of a tile. Tiles are numbered and thus a sokoban screen is the
-set $F$ containing a $x_i\in T$ for every tile. To encode the state we
-introduce an encoding function that encodes a state in three boolean variables:
+Let $T=\{free,box,target,agent,targetagent,targetbox\}$ be the set of possible
+states of a tile. Tiles are numbered and thus a sokoban screen is the set $F$
+containing a $x_i\in T$ for every tile. We introduce a function $ord(x, y)$
+that returns the tile number for a given $x$ and $y$ coordinate. To encode the
+state we introduce an encoding function that encodes a state in three boolean
+variables:
$$encode(t)=\begin{cases}
000 & \text{if }t=wall\\
001 & \text{if }t=free\\
\subsection{Transition encoding}
We introduce a variable denoting the intended direction of movement $m \in
-\{\text{up}, \text{down}, \text{left}, \text{right}\}$.
+\{\text{up}, \text{down}, \text{left}, \text{right}\}$. Tiles
%
%Let\\
%$\delta_{x}(x,m) =