Atropos-k is PSPACE-complete
Computational Complexity
2025-03-25 v1 Discrete Mathematics
Combinatorics
Abstract
Burke and Teng introduced a two-player combinatorial game Atropos based on Sperner's lemma, and showed that deciding whether one has a winning strategy for Atropos is PSPACE-complete. In the original Atropos game, the players must color a node adjacent to the last colored node. Burke and Teng also mentioned a variant Atropos-k in which each move is at most of distance k of the previous move, and asked a question on determining the computational complexity of this variant. In this paper, we answer this question by showing that for any fixed integer k (k>=2), Atropos-k is PSPACE-complete by reduction from True Quantified Boolean Formula (TQBF).
Cite
@article{arxiv.2403.01662,
title = {Atropos-k is PSPACE-complete},
author = {Chao Yang and Zhujun Zhang},
journal= {arXiv preprint arXiv:2403.01662},
year = {2025}
}