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Computational Complexity of Two-Dimensional Platform Games

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Fun with Algorithms (FUN 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6099))

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Abstract

We analyze the computational complexity of various two-dimensional platform games. We state and prove several meta-theorems that identify a class of these games for which the set of solvable levels is NP-hard, and another class for which the set is even PSPACE-hard. Notably CommanderKeen is shown to be NP-hard, and PrinceOfPersia is shown to be PSPACE-complete.

We then analyze the related game Lemmings, where we construct a set of instances which only have exponentially long solutions. This shows that an assumption by Cormode in [3] is false and invalidates the proof that the general version of the Lemmings decision problem is in NP. We then augment our construction to only include one entrance, which makes our instances perfectly natural within the context of the original game.

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Author information

Authors and Affiliations

  1. Comenius University, Bratislava, Slovakia

    Michal Forišek

Authors
  1. Michal Forišek
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Editors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, 20135, Milano, Italy

    Paolo Boldi

  2. Dip. di Informatica ed Applicazioni, Universitá di Salerno, 84084, Fisciano, Italy

    Luisa Gargano

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Forišek, M. (2010). Computational Complexity of Two-Dimensional Platform Games. In: Boldi, P., Gargano, L. (eds) Fun with Algorithms. FUN 2010. Lecture Notes in Computer Science, vol 6099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13122-6_22

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  • DOI: https://doi.org/10.1007/978-3-642-13122-6_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13121-9

  • Online ISBN: 978-3-642-13122-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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