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Deciding game invariance

Eric Duchene 1 Aline Parreau 1, 2 Michel Rigo 2
1 GOAL - Graphes, AlgOrithmes et AppLications
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : Duchêne and Rigo introduced the notion of invariance for take-away games on heaps. Roughly speaking, these are games whose rulesets do not depend on the position. Given a sequence S of positive tuples of integers, the question of whether there exists an invariant game having S as set of P-positions is relevant. In particular, it was recently proved by Larsson et al. that if $S$ is a pair of complementary Beatty sequences, then the answer to this question is always positive. In this paper, we show that for a fairly large set of sequences (expressed by infinite words), the answer to this question is decidable.
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https://hal.archives-ouvertes.fr/hal-01283830
Contributor : Eric Duchene <>
Submitted on : Sunday, March 6, 2016 - 10:15:39 PM
Last modification on : Thursday, November 21, 2019 - 2:29:18 AM

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Eric Duchene, Aline Parreau, Michel Rigo. Deciding game invariance. Information and Computation, Elsevier, 2017, 253 (1), pp.127-142. ⟨10.1016/j.ic.2017.01.010⟩. ⟨hal-01283830⟩

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