We consider the popular smartphone game Trainyard: a puzzle game that requires the player to lay down tracks in order to route colored trains from departure stations to suitable arrival stations. While it is already known [Almanza et al., FUN 2016] that the problem of finding a solution to a given Trainyard instance (i.e., game level) is NP-hard, determining the computational complexity of checking whether a candidate solution (i.e., a track layout) solves the level was left as an open problem. In this paper we prove that this verification problem is PSPACE-complete, thus implying that Trainyard players might not only have a hard time finding solutions to a given level, but they might even be unable to efficiently recognize them.
@InProceedings{almanza_et_al:LIPIcs.FUN.2018.4, author = {Almanza, Matteo and Leucci, Stefano and Panconesi, Alessandro}, title = {{Tracks from hell - when finding a proof may be easier than checking it}}, booktitle = {9th International Conference on Fun with Algorithms (FUN 2018)}, pages = {4:1--4:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-067-5}, ISSN = {1868-8969}, year = {2018}, volume = {100}, editor = {Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.4}, URN = {urn:nbn:de:0030-drops-87954}, doi = {10.4230/LIPIcs.FUN.2018.4}, annote = {Keywords: puzzle games, solitaire games, Trainyard, verification} }
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