Paper by Erik D. Demaine

Erik D. Demaine, Justin Kopinsky, and Jayson Lynch, “Recursed Is Not Recursive: A Jarring Result”, in Proceedings of the the 31st International Symposium on Algorithms and Computation (ISAAC 2020), Hong Kong, December 14–18, 2020, 35:1–35:15.

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 15 × 20 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.

This paper is also available from LIPIcs, and from arXiv. A sample level from the reduction is available on Github.

The paper is 15 pages.

The paper is available in PDF (1163k).
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Last updated January 15, 2021 by Erik Demaine.