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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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References

  1. Aaron B. Adcock, Erik D. Demaine, Martin L. Demaine, Michael P. O'Brien, Felix Reidl, Fernando Sánchez Villaamil, and Blair D. Sullivan. Zig-zag numberlink is np-complete. JIP, 23(3):239-245, 2015. URL: http://dx.doi.org/10.2197/ipsjjip.23.239.
  2. Matteo Almanza, Stefano Leucci, and Alessandro Panconesi. Trainyard is NP-hard. Theoretical Computer Science, 2017. URL: http://dx.doi.org/10.1016/j.tcs.2017.09.039.
  3. Joseph Culberson. Sokoban is PSPACE-complete. In Proceedings of the 1st International Conference on Fun with Algorithms (FUN'98), volume 4, pages 65-76, 1998. Google Scholar
  4. Giuseppe Pasolini dall'Onda and Pier Desiderio Pasolini. Memoir of Count Giuseppe Pasolini. Longmans, Green, and Company, 1885. Google Scholar
  5. David Eppstein. Computational complexity of games and puzzles. URL: https://www.ics.uci.edu/~eppstein/cgt/hard.html.
  6. Gary William Flake and Eric B. Baum. Rush hour is pspace-complete, or "why you should generously tip parking lot attendants". Theor. Comput. Sci., 270(1-2):895-911, 2002. URL: http://dx.doi.org/10.1016/S0304-3975(01)00173-6.
  7. Eric Goles, Pedro Montealegre, Ville Salo, and Ilkka Törmä. Pspace-completeness of majority automata networks. Theor. Comput. Sci., 609:118-128, 2016. URL: http://dx.doi.org/10.1016/j.tcs.2015.09.014.
  8. Luciano Gualà, Stefano Leucci, and Emanuele Natale. Bejeweled, candy crush and other match-three games are (np-)hard. In 2014 IEEE Conference on Computational Intelligence and Games, CIG 2014, Dortmund, Germany, August 26-29, 2014, pages 1-8. IEEE, 2014. URL: http://dx.doi.org/10.1109/CIG.2014.6932866.
  9. Luciano Gualà, Stefano Leucci, Emanuele Natale, and Roberto Tauraso. Large peg-army maneuvers. In Erik D. Demaine and Fabrizio Grandoni, editors, 8th International Conference on Fun with Algorithms, FUN 2016, June 8-10, 2016, La Maddalena, Italy, volume 49 of LIPIcs, pages 18:1-18:15. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.FUN.2016.18.
  10. Robert A. Hearn and Erik D. Demaine. Games, Puzzles, and Computation. CRC Press, 2009. Google Scholar
  11. Graham Kendall, Andrew J. Parkes, and Kristian Spoerer. A survey of np-complete puzzles. ICGA Journal, 31(1):13-34, 2008. Google Scholar
  12. Stefan Langerman and Yushi Uno. Threes!, fives, 1024!, and 2048 are hard. In Erik D. Demaine and Fabrizio Grandoni, editors, 8th International Conference on Fun with Algorithms, FUN 2016, June 8-10, 2016, La Maddalena, Italy, volume 49 of LIPIcs, pages 22:1-22:14. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.FUN.2016.22.
  13. Neeldhara Misra. Two dots is np-complete. In Erik D. Demaine and Fabrizio Grandoni, editors, 8th International Conference on Fun with Algorithms, FUN 2016, June 8-10, 2016, La Maddalena, Italy, volume 49 of LIPIcs, pages 24:1-24:12. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2016. URL: http://dx.doi.org/10.4230/LIPIcs.FUN.2016.24.
  14. Italia : Consiglio superiore dei lavori pubblici. Annali dei lavori pubblici. Eredi di A. De Gaetani. In italian. Google Scholar
  15. Ryuhei Uehara and Shigeki Iwata. Generalized Hi-Q is NP-complete. IEICE Transactions (1976-1990), 73(2):270-273, 1990. Google Scholar
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