PSPACE-Hard 2D Super Mario Games: Thirteen Doors

This paper was initiated during open problem solving in the MIT class on Algorithmic Lower Bounds: Fun with Hardness Proofs (6.5440), taught by Erik Demaine in Fall 2023; and during the 33rd Bellairs Winter Workshop on Computational Geometry, co-organized by Erik Demaine and Godfried Toussaint in March 2018 in Holetown, Barbados. We thank the other participants of that class and workshop for helpful discussions and providing an inspiring atmosphere. Much of the work in this paper would not have been possible without the wealth of tools created by the communities surrounding the Super Mario games. In particular, the following level editing and emulation tools were of immense importance to testing various gadget ideas and mechanics: - The NES Super Mario Brothers 2 Level Editor by loginsinex - https://github.com/loginsinex/smb2 - SMB3 Foundry by mchlnix - https://github.com/mchlnix/SMB3-Foundry - MarCas by Coolman - https://www.romhacking.net/utilities/518/ - Lunar Magic by FuSoYa - https://fusoya.eludevisibility.org/lm/ - Golden Egg by Romi - https://www.smwcentral.net/?p=section&a=details&id=4645 - Reggie! by the NSMBW Community - https://github.com/NSMBW-Community/Reggie-Updated - CoinKiller by Arisotura - https://github.com/Arisotura/CoinKiller - Miyamoto by aboood40091 - https://github.com/aboood40091/Miyamoto - BizHawk by TASEmulators - https://github.com/TASEmulators/BizHawk - Mesenrta by threecreepio - https://github.com/threecreepio/mesenrta - Mesenrta-s by threecreepio - https://github.com/threecreepio/mesenrta-s - mGBA by endrift - https://mgba.io/ - Dolphin by the Dolphin Emulator Project - https://dolphin-emu.org/ - Citra by Citra Team - https://citra-emu.org/ - Cemu by Team Cemu - https://cemu.info/