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Fundamentals of Parameterized Complexity pp 491–507Cite as

Fixed Parameter Analogues of PSpace and k-Move Games

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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.

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Notes

  1. 1.

    Some of them, such as the WK-hierarchy will be met in Chap. 30 and the M-hierarchy found in Chap. 29 are quite new and relate to lower bounds and strong complexity hypotheses.

  2. 2.

    Flum and Grohe argue that this makes the A-hierarchy a natural analogue of the polynomial time hierarchy. The other possible analogue according to our results would be the AW[t] hierarchy. Space considerations preclude us for a discussion, and we refer the reader to [312].

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Authors and Affiliations

  1. School of Mathematics, Statistics and Operations Research, Victoria University, Wellington, New Zealand

    Rodney G. Downey

  2. School of Engineering and Information Technology, Charles Darwin University, Darwin, Northern Territory, Australia

    Michael R. Fellows

Authors
  1. Rodney G. Downey
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  2. Michael R. Fellows
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Downey, R.G., Fellows, M.R. (2013). Fixed Parameter Analogues of PSpace and k-Move Games. In: Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-5559-1_26

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  • DOI: https://doi.org/10.1007/978-1-4471-5559-1_26

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5558-4

  • Online ISBN: 978-1-4471-5559-1

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