arXiv subjects

Hayashi Layers

Publications and source records attributed to Hayashi Layers.

3 recordsLinked to original sources

arXiv2024

You Can't Solve These Super Mario Bros. Levels: Undecidable Mario Games

We prove RE-completeness (and thus undecidability) of several 2D games in the Super Mario Bros. platform video game series: the New Super Mario Bros. series (original, Wii, U, and 2), and both Super Mario Maker games in all five game styles (Super Mario Bros. 1 and 3, Super Mario World, New Super Mario Bros. U, and Super Mario 3D World). These results hold even when we restrict to constant-size levels and screens, but they do require generalizing to allow arbitrarily many enemies at each location and onscreen, as well as allowing for exponentially large (or no) timer. Our New Super Mario Bros. constructions fit within one standard screen size. In our Super Mario Maker reductions, we work within the standard screen size and use the property that the game engine remembers offscreen objects that are global because they are supported by "global ground". To prove these Mario results, we build a new theory of counter gadgets in the motion-planning-through-gadgets framework, and provide a suite of simple gadgets for which reachability is RE-complete.

cs.CC↗

arXiv2024

PSPACE-Hard 2D Super Mario Games: Thirteen Doors

We prove PSPACE-hardness for fifteen games in the Super Mario Bros. 2D platforming video game series. Previously, only the original Super Mario Bros. was known to be PSPACE-hard (FUN 2016), though several of the games we study were known to be NP-hard (FUN 2014). Our reductions build door gadgets with open, close, and traverse traversals, in each case using mechanics unique to the game. While some of our door constructions are similar to those from FUN 2016, those for Super Mario Bros. 2, Super Mario Land 2, Super Mario World 2, and the New Super Mario Bros. series are quite different; notably, the Super Mario Bros. 2 door is extremely difficult. Doors remain elusive for just two 2D Mario games (Super Mario Land and Super Mario Run); we prove that these games are at least NP-hard.

cs.CC↗

arXiv2020

Walking through Doors is Hard, even without Staircases: Universality and PSPACE-hardness of Planar Door Gadgets

An open-close door gadget has two states and three tunnels that can be traversed by an agent (player, robot, etc.): the "opening" and "closing" tunnels set the gadget's state to open and closed, respectively, while the "traverse" tunnel can be traversed if and only if the door is in the open state. We prove that it is PSPACE-complete to decide whether an agent can move from one location to another through a planar system of any such door gadget, removing the traditional need for crossover gadgets and thereby simplifying past PSPACE-hardness proofs of Lemmings and Nintendo games Super Mario Bros., Legend of Zelda, and Donkey Kong Country. Even stronger, we show that any gadget in the motion-planning-through-gadgets framework can be simulated by a planar system of door gadgets: the open-close door gadget is a universal gadget. We prove that these results hold for a variety of door gadgets. In particular, the opening, closing, and traverse tunnel locations can have an arbitrary cyclic order around the door; each tunnel can be directed or undirected; and the opening tunnel can instead be an optional button (with identical entrance and exit locations). Furthermore, we show the same hardness and universality results for two simpler types of door gadgets: self-closing door gadgets and symmetric self-closing door gadgets. Again we show that any self-closing door gadget planarly simulates any gadget, and thus the reachability motion planning problem is PSPACE-complete. Then we apply this framework to prove new PSPACE-hardness results for eight different 3D Mario video games and Sokobond.

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