Recursed is not Recursive: A Jarring Result
This establishes computational complexity results for a real-world video game, showing it can simulate Turing machines.
The authors proved that the puzzle game Recursed is RE-complete and thus undecidable by reducing the Post Correspondence Problem to playable game levels, with the reduction being efficient in terms of level size and solution length.
Recursed is a 2D puzzle platform video game featuring treasure chests that, when jumped into, instantiate a room that can later be exited (similar to function calls), optionally generating a jar that returns back to that room (similar to continuations). We prove that Recursed is RE-complete and thus undecidable (not recursive) by a reduction from the Post Correspondence Problem. Our reduction is "practical": the reduction from PCP results in fully playable levels that abide by all constraints governing levels (including the 15x20 room size) designed for the main game. Our reduction is also "efficient": a Turing machine can be simulated by a Recursed level whose size is linear in the encoding size of the Turing machine and whose solution length is polynomial in the running time of the Turing machine.