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Solving the Sabotage Game Is PSPACE-Hard

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Mathematical Foundations of Computer Science 2003 (MFCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2747))

Abstract

We consider the sabotage game as presented by van Benthem. In this game one player moves along the edges of a finite multi-graph and the other player takes out a link after each step. One can consider usual algorithmic tasks like reachability, Hamilton path, or complete search as winning conditions for this game. As the game definitely ends after at most the number of edges steps, it is easy to see that solving the sabotage game for the mentioned tasks takes at most PSPACE in the size of the graph. In this paper we establish the PSPACE-hardness of this problem. Furthermore, we introduce a modal logic over changing models to express tasks corresponding to the sabotage games and we show that model checking this logic is PSPACE-complete.

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References

  1. van Benthem, J.: An essay on sabotage and obstruction. In: Hutter, D., Werner, S. (eds.) Festschrift in Honour of Prof. Jörg Siekmann. LNCS (LNAI), Springer, Heidelberg (2002)

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  2. Demaine, E.D.: Playing games with algorithms: Algorithmic combinatorial game theory. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 18–32. Springer, Heidelberg (2001)

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  3. Papadimitriou, C.H.: Computational Complexity. Addison–Wesley, London (1994)

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  4. Löding, C., Rohde, P.: Solving the sabotage game is PSPACE-hard. Technical Report AIB-05-2003, RWTH Aachen (2003)

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Authors and Affiliations

  1. Lehrstuhl für Informatik VII, RWTH Aachen,  

    Christof Löding & Philipp Rohde

Authors
  1. Christof Löding
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  2. Philipp Rohde
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Editors and Affiliations

  1. Department of Computer Science, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovakia

    Branislav Rovan

  2. Charles University, Prague, Czech Republic

    Peter Vojtáš

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© 2003 Springer-Verlag Berlin Heidelberg

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Löding, C., Rohde, P. (2003). Solving the Sabotage Game Is PSPACE-Hard. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_47

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  • DOI: https://doi.org/10.1007/978-3-540-45138-9_47

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40671-6

  • Online ISBN: 978-3-540-45138-9

  • eBook Packages: Springer Book Archive

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