I really thought that all human-initiated action had been removed from the Magic machine. Oops. It's been a while since I read the complete writeup. But it looks like it should be possible to fix this.
What I find really cool is that, while they might not add a set of cards allowing for arbitrary branching, they could introduce cards that allow for some bounded branching. This could add limitations of resource bounds that are still scalable: polynomial time, space, exponential time, primitive recursion. There seems to be a lot more flexibility here than with some other mentioned "Turing-Complete" systems.
Someone else, here, commented that you would also need to implement infinite loops. Assuming you don't have to fuel the machine with cards, this method could be used to stall a real game indefinitely! Apparently this is possible. O_O
Just like a theoretical Turing machine doesn't require a human to feed it with a strip of tape, a theoretical Magic-Turing machine doesn't require a human to feed it with tokens and damage markers.
And game-breaking infinite loops in Magic are dime a dozen. Did you know that there's a combo that allows you to rip every card in your opponent's deck into confetti? (Unless they forfeit.)
Sorry if I entirely missed the point of what you were saying.
I must have not been clear and concise. I apologize for this. I was discussing the scenario where we introduce a set of cards that allow for an arbitrary number of triggers without human involvement. We clearly need to implement a way of handling nested loops, branching, and recursive calls. So the set of cards facilitating this need to either need to do this completely by themselves or construct the behavior given the state of the playing field. I did not assume we can do what is described in the paper (the site) because I have no reason to think the new cards must function in a way that is compatible with their setup. This is why I am interested in the possibility of implicit and bounded recursion.
The fuel comment was just relevant to implementing an infinite loop in a real game. If our supposed 100% autonomous system (with the new cards as mentioned above) relied on an additional resource (such as burning through cards each "tick"), then this wouldn't work in real life but would work if we generalized the size of the deck or available cards. This is not supposed to be a characteristic of Turing Machines in general (or at all). It was just a precaution for attempting to translate an instance of the generalized case to real life.
If your answer is no, then I think the current cards are already sufficient, it just needs some clever finagling to take the current design and remove all 'may' choices.
If your answer is yes then I think your standards are flawed.
>Could you link something describing the hilarious confetti combo?
Okay, looking into it it was less of a loop than I thought: http://www.mtgvault.com/doompie/decks/the-deck-ripper/
So I got you this instead: http://www.mtgvault.com/planestalker/decks/16-infinite-loops...
As for whether or not the current cards suffice, I can't say much (I don't care about Magic tbh). It just speculation as far as I can tell. I was not presuming that new cards are necessary. I just considered it for the sake of the hypothetical.
Interesting links. Thank you.