If you can start on any top row location, and finish on any bottow row location, the problems doesn't at all become much more complex and time consuming. Just add two more nodes to the maze: a start node with exits to all the valid top row locations, and a finish node, with entries from all the valid bottow row locations, and you have a "standard maze" again, with 1 start, and 1 end position.

Now, why on earth you are referring to the AI or finite automata to solve this problem is beyond me. It's a graph problem, all you want is a path from one end to the other, and if there are multiple paths, you want to find a minimal one using some measurement.

Abigail