Undecidability of Two-dimensional Robot Games



Potapov, I, Niskanen, R ORCID: 0000-0002-2210-1481 and Reichert, J
(2016) Undecidability of Two-dimensional Robot Games. In: 41st International Symposium on Mathematical Foundations of Computer Science, 2016-08-22 - 2016-08-26, Krakow (Poland).

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Abstract

Robot game is a two-player vector addition game played on the integer lattice Z^n. Both players have sets of vectors and in each turn the vector chosen by a player 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 undecidability of the robot game in dimension two answering the question formulated by Doyen and Rabinovich in 2011 and closing the gap between undecidable and decidable cases.

Item Type: Conference or Workshop Item (Unspecified)
Uncontrolled Keywords: reachability games, vector addition game, decidability, winning strategy
Depositing User: Symplectic Admin
Date Deposited: 27 Jun 2016 14:45
Last Modified: 26 Apr 2022 11:32
DOI: 10.4230/LIPIcs.MFCS.2016.73
URI: https://livrepository.liverpool.ac.uk/id/eprint/3001838