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Robot Games with States in Dimension One

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Book cover Reachability Problems (RP 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9899))

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Abstract

A robot game with states is a two-player vector addition game played on integer lattice \(\mathbb {Z}^n\). Both players have their own control states and in each turn the vector chosen by a player, according to his/her internal control structure, is added to the current configuration vector of the game. One of the players, called Eve, tries to play the game from the initial configuration to the origin while the other player, Adam, tries to avoid the origin. The problem is to decide whether or not Eve has a winning strategy. In this paper we prove that deciding the winner in a robot game with states in dimension one is EXPSPACE-complete. Additionally we study a subclass of robot games with states where deciding the winner is in EXPTIME.

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Acknowledgements

The author would like to thank Igor Potapov for proposing the topic and helpful discussions.

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Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, UK

    Reino Niskanen

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  1. Reino Niskanen
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Correspondence to Reino Niskanen .

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Editors and Affiliations

  1. Aalborg University, Aalborg, Denmark

    Kim Guldstrand Larsen

  2. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

  3. Aalborg University, Aalborg, Denmark

    Jiří Srba

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Niskanen, R. (2016). Robot Games with States in Dimension One. In: Larsen, K., Potapov, I., Srba, J. (eds) Reachability Problems. RP 2016. Lecture Notes in Computer Science(), vol 9899. Springer, Cham. https://doi.org/10.1007/978-3-319-45994-3_12

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  • DOI: https://doi.org/10.1007/978-3-319-45994-3_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45993-6

  • Online ISBN: 978-3-319-45994-3

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