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LaserTank is NP-Complete

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Mathematical Aspects of Computer and Information Sciences (MACIS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11989))

Abstract

We show that the classical game LaserTank is \(\mathrm {NP}\)-complete, even when the tank movement is restricted to a single column and the only blocks appearing on the board are mirrors and solid blocks. We show this by reducing 3-SAT instances to LaserTank puzzles.

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Notes

  1. 1.

    https://en.wikipedia.org/wiki/LaserTank.

  2. 2.

    https://www.ticalc.org/archives/files/fileinfo/95/9532.html.

  3. 3.

    For a complete list of pieces available in the official game, see https://lasertanksolutions.blogspot.com/p/in-my-opinionlaser-tank-is-best-logic.html.

References

  1. Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the Third Annual ACM Symposium on Theory of Computing, STOC 1971, pp. 151–158. ACM, New York (1971). https://doi.org/10.1145/800157.805047

  2. Demaine, E.D., Hohenberger, S., Liben-Nowell, D.: Tetris is hard, even to approximate. Technical report, MIT-LCS-TR-865. MIT, Cambridge (2002). https://arxiv.org/abs/cs/0210020

  3. Dor, D., Zwick, U.: SOKOBAN and other motion planning problems. Comput. Geom. 13(4), 215–228 (1999). https://doi.org/10.1016/s0925-7721(99)00017-6

    Article  MathSciNet  MATH  Google Scholar 

  4. Flake, G.W., Baum, E.B.: Rush Hour is PSPACE-complete, or “Why you should generously tip parking lot attendants”. Theor. Comput. Sci. 270(1–2), 895–911 (2002). https://doi.org/10.1016/s0304-3975(01)00173-6

    Article  MathSciNet  MATH  Google Scholar 

  5. Kaye, R.: Minesweeper is NP-complete. Math. Intell. 22(2), 9–15 (2000). https://doi.org/10.1007/bf03025367

    Article  MathSciNet  MATH  Google Scholar 

  6. Scott, A., Stege, U., van Rooij, I.: Minesweeper may not be NP-complete but is hard nonetheless. Math. Intell. 33(4), 5–17 (2011). https://doi.org/10.1007/s00283-011-9256-x

    Article  MathSciNet  MATH  Google Scholar 

  7. Viglietta, G.: Gaming is a hard job, but someone has to do it! Theory Comput. Syst. 54(4), 595–621 (2013). https://doi.org/10.1007/s00224-013-9497-5

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Acknowledgements

This work was partially supported by the Wallenberg AI, Autonomous System and Software Program (WASP) founded by the Knut and Alice Wallenberg Foundation.

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Authors and Affiliations

  1. KTH The Royal Institute of Technology, 100 44, Stockholm, Sweden

    Per Alexandersson & Petter Restadh

Authors
  1. Per Alexandersson
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  2. Petter Restadh
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Corresponding author

Correspondence to Petter Restadh .

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Editors and Affiliations

  1. AIT Austrian Institute of Technology, Vienna, Austria

    Daniel Slamanig

  2. IMJ-PRG, Sorbonne University, Paris, France

    Elias Tsigaridas

  3. Institute of Information Technologies, Gebze Technical University, Gebze, Turkey

    Zafeirakis Zafeirakopoulos

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Alexandersson, P., Restadh, P. (2020). LaserTank is NP-Complete. In: Slamanig, D., Tsigaridas, E., Zafeirakopoulos, Z. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science(), vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_26

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  • DOI: https://doi.org/10.1007/978-3-030-43120-4_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43119-8

  • Online ISBN: 978-3-030-43120-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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