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Solving the Sabotage Game Is PSPACE-Hard

  • Christof Löding
  • Philipp Rohde
Part of the Lecture Notes in Computer Science book series (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.

Keywords

Model Check Modal Logic Undirected Graph Hamilton Path Winning Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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)Google Scholar
  2. 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)CrossRefGoogle Scholar
  3. 3.
    Papadimitriou, C.H.: Computational Complexity. Addison–Wesley, London (1994)zbMATHGoogle Scholar
  4. 4.
    Löding, C., Rohde, P.: Solving the sabotage game is PSPACE-hard. Technical Report AIB-05-2003, RWTH Aachen (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Christof Löding
    • 1
  • Philipp Rohde
    • 1
  1. 1.Lehrstuhl für Informatik VIIRWTH Aachen 

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