Robot Games with States in Dimension One

  • Reino NiskanenEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9899)


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.


Reachability games Vector addition game Decidability Winning strategy 



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


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK

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