2 Assumptions

A maze is made from square cells. The set of all cells in a maze is $C$. A ``mouse'' in the maze can only move in north, east, south or west direction. No diagonal move is permitted. Turn time as assumed to be 0. It takes the same amount of time to move from one cell to its adjacent neighbor, regardless of direction.

Adjacent neighbors can be blocked by a partition. If two adjacent neighboring cells are blocked, the mouse cannot move directly from one to the other one. The predicate $P(c,d)$ is true if and only if cells $c$ and $d$ are adjacent, and they are not blocked by a partition. The open neighbor set of a cell $c$ is defined as $O(c)=\{x\vert x \in C, P(c,x)\}$.

There is one or more destination cells in the maze. The set of all destination cells is $D$. Obviously, $D \subseteq C$.