Deciding game invariance
Discrete Mathematics
2014-08-25 v1 Computational Complexity
Combinatorics
Abstract
Duch\^ene 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 of positive tuples of integers, the question of whether there exists an invariant game having as set of -positions is relevant. In particular, it was recently proved by Larsson et al. that if 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.
Cite
@article{arxiv.1408.5274,
title = {Deciding game invariance},
author = {Eric Duchêne and Aline Parreau and Michel Rigo},
journal= {arXiv preprint arXiv:1408.5274},
year = {2014}
}