Here is a simple disproof of the control question.
Among the possible ways the rest of the grid could be filled, one is that is it empty except for the diagonally opposite corner, where there is a duplicate of the top left corner, rotated 180 degrees. Since this makes the whole grid symmetrical under that rotation, every future state must also be symmetrical. The smiley does not have that symmetry, therefore it cannot be achieved.
Yeah success with high probability was how I thought the question would need to be amended to deal with the case of multiple AIs. I mentioned this in the appendix but should have put it in the main text. Will add a note.
Here is a simple disproof of the control question.
Among the possible ways the rest of the grid could be filled, one is that is it empty except for the diagonally opposite corner, where there is a duplicate of the top left corner, rotated 180 degrees. Since this makes the whole grid symmetrical under that rotation, every future state must also be symmetrical. The smiley does not have that symmetry, therefore it cannot be achieved.
Also, what Charlie Steiner said.
My understanding was that we just want to succeed with high probability. The vast majority of configurations will not contain enemy AIs.
Yeah success with high probability was how I thought the question would need to be amended to deal with the case of multiple AIs. I mentioned this in the appendix but should have put it in the main text. Will add a note.