Restricted Power - Computational Complexity Results for Strategic Defense Games

Authors Ronald de Haan , Petra Wolf



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Author Details

Ronald de Haan
  • Institute for Logic, Language and Computation, University of Amsterdam, the Netherlands
Petra Wolf
  • Wilhelm-Schickard-Institut, University of Tübingen, Germany

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Ronald de Haan and Petra Wolf. Restricted Power - Computational Complexity Results for Strategic Defense Games. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FUN.2018.17

Abstract

We study the game Greedy Spiders, a two-player strategic defense game, on planar graphs and show PSPACE-completeness for the problem of deciding whether one player has a winning strategy for a given instance of the game. We also generalize our results in metatheorems, which consider a large set of strategic defense games. We achieve more detailed complexity results by restricting the possible strategies of one of the players, which leads us to Sigma^p_2- and Pi^p_2-hardness results.

Subject Classification

ACM Subject Classification
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Computational complexity
  • generalized games
  • metatheorems

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References

  1. Blizzard Entertainment: Warcraft III. http://eu.blizzard.com/en-gb/games/war3/. Accessed: 2018-02-17.
  2. Bloons Tower Defense 5. http://bloons.wikia.com/wiki/Bloons_Tower_Defense_5. Accessed: 2018-02-17.
  3. Greedy Spiders. http://greedyspiders.com/. Accessed: 2018-02-17.
  4. Nintendo Entertainment System (NES). http://www.pcgames.de/Nintendo-Entertainment-System-NES-Konsolen-255246/. Accessed: 2018-02-01.
  5. StarCraft: Remastered. https://starcraft.com/en-us/. Accessed: 2018-02-17.
  6. Greg Aloupis, Erik D. Demaine, Alan Guo, and Giovanni Viglietta. Classic Nintendo Games are (Computationally) Hard. Theoretical Computer Science, 586:135-160, 2015. Google Scholar
  7. Sanjeev Arora and Boaz Barak. Computational Complexity - A Modern Approach. Cambridge University Press, 2009. Google Scholar
  8. Ashok K. Chandra, Dexter C. Kozen, and Larry J. Stockmeyer. Alternation. J. of the ACM, 28(1):114-133, 1981. Google Scholar
  9. Erik D. Demaine. Playing Games with Algorithms: Algorithmic Combinatorial Game Theory. In Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science (MFCS), pages 18-33. Springer, 2001. Google Scholar
  10. Erik D. Demaine and Robert A. Hearn. Constraint Logic: A Uniform Framework for Modeling Computation as Games. In Proceedings of the 23rd Annual IEEE Conference on Computational Complexity, 2008 (CCC 2008), pages 149-162. IEEE, 2008. Google Scholar
  11. Erik D. Demaine, Joshua Lockhart, and Jayson Lynch. The Computational Complexity of Portal and Other 3D Video Games. arXiv preprint 1611.10319, 2016. Google Scholar
  12. Michal Forišek. Computational Complexity of Two-Dimensional Platform Games. In Proceedings of the 5th International Conference on Fun with Algorithms (FUN 2010), pages 214-227. Springer, 2010. Google Scholar
  13. Graham Kendall, Andrew J. Parkes, and Kristian Spoerer. A Survey of NP-complete Puzzles. ICGA Journal, 31(1):13-34, 2008. Google Scholar
  14. David Lichtenstein. Planar Formulae and Their Uses. SIAM J. Comput., 11(2):329-343, 1982. Google Scholar
  15. John Michael Robson. The Complexity of Go. In IFIP Congress, pages 413-417, 1983. Google Scholar
  16. John Michael Robson. N by N Checkers is Exptime complete. SIAM J. Comput., 13(2):252-267, 1984. Google Scholar
  17. Jörg Siekmann and Graham Wrightson, editors. Automation of reasoning. Classical Papers on Computer Science 1967-1970, volume 2. 1983. Google Scholar
  18. G. S. Tseitin. Complexity of a Derivation in the Propositional Calculus. Zap. Nauchn. Sem. Leningrad Otd. Mat. Inst. Akad. Nauk SSSR, 8:23-41, 1968. English transl. repr. in [17]. Google Scholar
  19. Giovanni Viglietta. Gaming is a hard job, but someone has to do it! Theory Comput. Syst., 54(4):595-621, 2014. URL: http://dx.doi.org/10.1007/s00224-013-9497-5.
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