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Recursed Is Not Recursive: A Jarring Result

Authors Erik D. Demaine , Justin Kopinsky, Jayson Lynch

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Author Details

Erik D. Demaine
  • Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, MA, USA
Justin Kopinsky
  • Work done while at MIT, Cambridge, MA, USA
Jayson Lynch
  • Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, MA, USA

Acknowledgements

This work was initiated 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 - in particular, Robert Hearn - for related discussions and providing an inspiring atmosphere. We thank Edison Y. He for his helpful comments on earlier drafts of this paper. Figures were generated using SVG Tiler [Demaine, 2020].

Cite As Get BibTex

Erik D. Demaine, Justin Kopinsky, and Jayson Lynch. Recursed Is Not Recursive: A Jarring Result. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 50:1-50:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ISAAC.2020.50

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Computational Complexity
  • Undecidable
  • Video Games

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References

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