I suspect you're probably right about it being difficult-nigh-impossible to do in a 3x3, but I think the silicon cube comment is a bit too doubting Thomas. Then again, I've never gotten into dwarfputing and probably never will, so grain of salt and all that.
I suspect it might involve storing a series of inputs and looking for similar patterns, like DAISY does, but I'm not sure how one would go about doing that in DF. I can kind of see having multiple levels of displays to keep track of past inputs, but I don't know about the patternfinding aspect.
At any rate, I wish you luck!
And of course, the next step if it does succeed is to build a real-world version. Because a semi-intelligent tower of stone that one communicates with through levers and trapdoors is kind of brilliant.