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Fixed Parameter Analogues of PSpace and k-Move Games

  • Rodney G. Downey
  • Michael R. Fellows
Part of the Texts in Computer Science book series (TCS)

Abstract

We define parameterized complexity classes that allow us to investigate the complexity of k-move games. We establish a number of concrete hardness and completeness results for games such as the k-move versions of Geography and Chess. We relate these classes to bounded space computations.

Keywords

Turing Machine Conjunctive Normal Form Winning Strategy Boolean Formula Conjunctive Query 
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.

References

  1. 2.
    K. Abrahamson, R. Downey, M. Fellows, Fixed-parameter intractability II, in Proceedings of 10th Annual Symposium on Theoretical Aspects on Computer Science, STACS 93, Würzburg, Germany, February 25–27, 1993, ed. by P. Enjalbert, A. Finkel, K. Wagner. LNCS, vol. 665 (Springer, Berlin, 1993), pp. 374–385 Google Scholar
  2. 3.
    K. Abrahamson, R. Downey, M. Fellows, Fixed-parameter tractability and completeness. IV. On completeness for W[P] and PSPACE analogues. Ann. Pure Appl. Log. 73(3), 235–276 (1995) MathSciNetCrossRefzbMATHGoogle Scholar
  3. 67.
    H. Björklund, S. Sandberg, S. Vorobyov, On fixed-parameter complexity of infinite games, in The Nordic Workshop on Programming Theory (NWPT’03), Åbo Akademi University, Turku, Finland, October 29–31, 2003, ed. by K. Sere, M. Waldén, A. Karlsson (Åbo Akademi, Department of Computer Science, Turku, 2003), pp. 62–64 Google Scholar
  4. 122.
    L. Cai, J. Chen, R. Downey, M. Fellows, Advice classes of parameterized tractability. Ann. Pure Appl. Log. 84, 119–138 (1997) MathSciNetCrossRefzbMATHGoogle Scholar
  5. 143.
    J. Chen, X. Huang, I. Kanj, G. Xia, On the computational hardness based on linear FPT-reductions. J. Comb. Optim. 11(2), 231–247 (2006) MathSciNetCrossRefzbMATHGoogle Scholar
  6. 153.
    Y. Chen, J. Flum, M. Grohe, Bounded nondeterminism and alternation in parameterized complexity theory, in Proceedings of the 18th Annual IEEE Conference on Computational Complexity, CCC 2003, Aarhus, Denmark, July 7–10, 2003 (IEEE Comput. Soc., Los Alamitos, 2003), pp. 13–29 CrossRefGoogle Scholar
  7. 243.
    R. Downey, M. Fellows, Fixed-parameter tractability and completeness. I. Basic results. SIAM J. Comput. 24(4), 873–921 (1995) MathSciNetCrossRefzbMATHGoogle Scholar
  8. 247.
    R. Downey, M. Fellows, Parameterized Complexity. Monographs in Computer Science (Springer, Berlin, 1999) CrossRefGoogle Scholar
  9. 256.
    R. Downey, M. Fellows, K. Regan, Parameterized circuit complexity and the W hierarchy. Theor. Comput. Sci. 191(1–2), 97–115 (1998) MathSciNetCrossRefzbMATHGoogle Scholar
  10. 258.
    R. Downey, M. Fellows, U. Taylor, The parameterized complexity of relational database queries and an improved characterization of W[1], in Combinatorics, Complexity & Logic, Proceedings of DMTCS ’96, Singapore, ed. by D. Bridges, C. Calude, J. Gibbons, S. Reeves, I. Witten (Springer, Berlin, 1996), pp. 194–213 Google Scholar
  11. 280.
    S. Even, R. Tarjan, A combinatorial problem which is complete for polynomial space. J. ACM 23, 710–719 (1976) MathSciNetzbMATHGoogle Scholar
  12. 309.
    J. Flum, M. Grohe, Fixed-parameter tractability, definability, and model checking. SIAM J. Comput. 31(1), 113–145 (2001) MathSciNetCrossRefzbMATHGoogle Scholar
  13. 312.
    J. Flum, M. Grohe, Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series (Springer, Berlin, 2006) Google Scholar
  14. 313.
    J. Flum, M. Grohe, M. Weyer, Bounded fixed-parameter tractability and log2 n nondeterministic bits. J. Comput. Syst. Sci. 72(1), 34–71 (2006) MathSciNetCrossRefzbMATHGoogle Scholar
  15. 337.
    M. Garey, D. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979) zbMATHGoogle Scholar
  16. 602.
    T. Schaefer, Complexity of some two-person perfect information games. J. Comput. Syst. Sci. 16(2), 185–225 (1978) MathSciNetCrossRefzbMATHGoogle Scholar
  17. 608.
    A. Scott, U. Stege, Parameterized chess, in Parameterized and Exact Computation, Proceedings of Third International Workshop, IWPEC ’08, Victoria, Canada, May, 2008, ed. by M. Grohe, R. Niedermeier. LNCS, vol. 5018 (Springer, Berlin, 2008), pp. 172–189 CrossRefGoogle Scholar
  18. 609.
    A. Scott, U. Stege, Parameterized pursuit-evasion games. Theor. Comput. Sci. 411(43), 3845–3858 (2010) MathSciNetCrossRefzbMATHGoogle Scholar
  19. 630.
    L. Stockmeyer, D. Kozen, A. Chandra, Alternation. J. ACM 28, 114–133 (1981) MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Rodney G. Downey
    • 1
  • Michael R. Fellows
    • 2
  1. 1.School of Mathematics, Statistics and Operations ResearchVictoria UniversityWellingtonNew Zealand
  2. 2.School of Engineering and Information TechnologyCharles Darwin UniversityDarwinAustralia

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