This is ridiculous. The real maps in these games didn't include even a hint of this kind of branching nonsense, so this kind of result says nothing about the actual difficulty of these games. And yet I sadly suspect "Zelda is NPC" is now going to become Internet folk wisdom. Groan. This paper is actively harmful if you ask me.
Classic Nintendo Games are NP-Hard
11–20 of 21 posts
Re: Classic Nintendo Games are NP-Hard
#12This is ridiculous. The real maps in these games didn't include even a hint of this kind of branching nonsense, so this kind of result says nothing about the actual difficulty of these games. And yet I sadly suspect "Zelda is NPC" is now going to become Internet folk wisdom. Groan. This paper is actively harmful if you ask me.
It's not about the actual difficulty of the games, it's about what sort of problems can be encoded using the gameplay.
Re: Classic Nintendo Games are NP-Hard
#13This is ridiculous. The real maps in these games didn't include even a hint of this kind of branching nonsense, so this kind of result says nothing about the actual difficulty of these games. And yet I sadly suspect "Zelda is NPC" is now going to become Internet folk wisdom. Groan. This paper is actively harmful if you ask me.
Any time I see papers like this, I'm reminded of Vargomax V. Vargomax's classic SIGBOVIK 2007 paper [1]. The presentation is also entertaining [2].
[1] http://www.cs.cmu.edu/~tom7/sigbovik/mariox.pdf [2] http://www.youtube.com/watch?v=HhGI-GqAK9c
Re: Classic Nintendo Games are NP-Hard
#14It's worth pointing out that even tic-tac-toe is PSPACE-complete. Here is a StackExchange question discussing the "solvability" of PSPACE vs NP: http://cstheory.stackexchange.com/questions/5323/are-pspace-...
Re: Classic Nintendo Games are NP-Hard
#15This is ridiculous. The real maps in these games didn't include even a hint of this kind of branching nonsense, so this kind of result says nothing about the actual difficulty of these games. And yet I sadly suspect "Zelda is NPC" is now going to become Internet folk wisdom. Groan. This paper is actively harmful if you ask me.
NP-completeness doesn't say anything about the difficulty of a specific instance of a given problem. It's trivial to construct CNF formulas that are solvable in polynomial time, for example.
An algorithm that is able to determine for every Zelda level, in polynomial time, whether or not the exit can be reached from the start is something quite different. As shown in this paper, this would imply that the same algorithm can solve every instance of every problem in NP efficiently, a.k.a. answer the million dollar question.
A cleaner way of stating the results of the paper would be: "The puzzle mechanics of Zelda are NPC". This statement is harder to misread, though I wouldn't hold my breath given the extreme illiteracy concerning theoretical computer science prevalent even among programmers with a degree, never mind the internet.
Re: Classic Nintendo Games are NP-Hard
#16This is ridiculous. The real maps in these games didn't include even a hint of this kind of branching nonsense, so this kind of result says nothing about the actual difficulty of these games. And yet I sadly suspect "Zelda is NPC" is now going to become Internet folk wisdom. Groan. This paper is actively harmful if you ask me.
The key word in the original paper (from 2012 (!)) is "Generalized".
IIRC, it's trivial that to "solve" Zelda Polynomial time (with an emulator) -- the entire state space of the console can be represented in constant space, so a trivial algorithm would be to traverse the state space tree with breadth-first search.
Re: Classic Nintendo Games are NP-Hard
#17This is ridiculous. The real maps in these games didn't include even a hint of this kind of branching nonsense, so this kind of result says nothing about the actual difficulty of these games. And yet I sadly suspect "Zelda is NPC" is now going to become Internet folk wisdom. Groan. This paper is actively harmful if you ask me.
NP-completeness doesn't say anything about the difficulty of a specific instance of a given problem. It's trivial to construct CNF formulas that are solvable in polynomial time, for example. An algorithm that is able to determine for every Zelda level, in polynomial time, whether or not the exit can be reached from the start is something quite different. As shown in this paper, this would imply that the same algorith…
Zelda is not simply a single instance of a static puzzle with a well-defined solution, it has code creating things dynamically. The title implies that the NP-complete problems are part of the actual gameplay. If you're only looking at mechanics you can pick nearly any game with movement and pull out traveling salesman.
Re: Classic Nintendo Games are NP-Hard
#18This is ridiculous. The real maps in these games didn't include even a hint of this kind of branching nonsense, so this kind of result says nothing about the actual difficulty of these games. And yet I sadly suspect "Zelda is NPC" is now going to become Internet folk wisdom. Groan. This paper is actively harmful if you ask me.
The key word in the original paper (from 2012 (!)) is "Generalized". IIRC, it's trivial that to "solve" Zelda Polynomial time (with an emulator) -- the entire state space of the console can be represented in constant space, so a trivial algorithm would be to traverse the state space tree with breadth-first search.
Picking a 'constant' of 2^k, with k the entire memory space of the console, is a rather inaccurate representation. It's like arguing that a desktop computer is not turing complete: true in such a narrow sense that using it to win a bar bet is going to lead to someone getting punched in the face.
Re: Classic Nintendo Games are NP-Hard
#19Earlier quoted context omitted.
NP-completeness doesn't say anything about the difficulty of a specific instance of a given problem. It's trivial to construct CNF formulas that are solvable in polynomial time, for example. An algorithm that is able to determine for every Zelda level, in polynomial time, whether or not the exit can be reached from the start is something quite different. As shown in this paper, this would imply that the same algorith…
Zelda is not simply a single instance of a static puzzle with a well-defined solution, it has code creating things dynamically. The title implies that the NP-complete problems are part of the actual gameplay. If you're only looking at mechanics you can pick nearly any game with movement and pull out traveling salesman.
I had this argument with my brother too, who is a mathematician. He was able to enjoy it on its own terms, I wasn't.
As he concluded, "they couldn't solve an interesting problem, so they solved an uninteresting one instead."
And from a certain stance, these fabricated problems do hold a bit of interest, especially when you consider how many mathematicians go out of their way to be impractical. Referencing the games confuses their work more than anything else, though.
Re: Classic Nintendo Games are NP-Hard
#20Earlier quoted context omitted.
NP-completeness doesn't say anything about the difficulty of a specific instance of a given problem. It's trivial to construct CNF formulas that are solvable in polynomial time, for example. An algorithm that is able to determine for every Zelda level, in polynomial time, whether or not the exit can be reached from the start is something quite different. As shown in this paper, this would imply that the same algorith…
Zelda is not simply a single instance of a static puzzle with a well-defined solution, it has code creating things dynamically. The title implies that the NP-complete problems are part of the actual gameplay. If you're only looking at mechanics you can pick nearly any game with movement and pull out traveling salesman.
A straight up implementation of TSP (I assume you mean the decision variant) needs some kind of door that shuts with a timer.
How do you plan to encode arbitrary graphs? This poses a challenge for 2d platformers. In case of any 2d game, how do you encode non-planar graphs? You would need some kind of teleportation device.
A graph with few edges and large edge values will also be problematic if you plan on keeping your input size polynomial (in |V| and |E|), as you'd need a widget capable of encoding an arbitrarily long edge in constant map space.
Once you have solved all the above problems, feel free to write a paper about it ;).