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Tracks from hell - when finding a proof may be easier than checking it

Authors Matteo Almanza, Stefano Leucci , Alessandro Panconesi

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Author Details

Matteo Almanza
  • Dipartimento di Informatica, Sapienza Università di Roma, Italy.
Stefano Leucci
  • Institute of Theoretical Computer Science, ETH Zürich, Switzerland.
Alessandro Panconesi
  • Dipartimento di Informatica, Sapienza Università di Roma, Italy.

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Matteo Almanza, Stefano Leucci, and Alessandro Panconesi. Tracks from hell - when finding a proof may be easier than checking it. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 4:1-4:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FUN.2018.4

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • puzzle games
  • solitaire games
  • Trainyard
  • verification

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