License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2020.50
URN: urn:nbn:de:0030-drops-133940
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13394/
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Demaine, Erik D. ; Kopinsky, Justin ; Lynch, Jayson

Recursed Is Not Recursive: A Jarring Result

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LIPIcs-ISAAC-2020-50.pdf (1 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{demaine_et_al:LIPIcs:2020:13394,
  author =	{Erik D. Demaine and Justin Kopinsky and Jayson Lynch},
  title =	{{Recursed Is Not Recursive: A Jarring Result}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{50:1--50:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Yixin Cao and Siu-Wing Cheng and Minming Li},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13394},
  URN =		{urn:nbn:de:0030-drops-133940},
  doi =		{10.4230/LIPIcs.ISAAC.2020.50},
  annote =	{Keywords: Computational Complexity, Undecidable, Video Games}
}

Keywords: Computational Complexity, Undecidable, Video Games
Collection: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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