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LaserTank is NP-Complete

  • Per Alexandersson
  • Petter RestadhEmail author
Conference paper
  • 32 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

NP-completeness LaserTank 3-SAT 

Notes

Acknowledgements

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

References

  1. 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. 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. 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)00017-6CrossRefMathSciNetzbMATHGoogle Scholar
  4. 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)00173-6CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    Kaye, R.: Minesweeper is NP-complete. Math. Intell. 22(2), 9–15 (2000).  https://doi.org/10.1007/bf03025367CrossRefMathSciNetzbMATHGoogle Scholar
  6. 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-xCrossRefMathSciNetzbMATHGoogle Scholar
  7. 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

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.KTH The Royal Institute of TechnologyStockholmSweden

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