Recursed is not Recursive: A Jarring Result

02/12/2020

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by   Erik Demaine, et al.

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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 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.